Both the NRSV and NIV are united to mislead us about the translation of pistis christou in Gal 2:16, 20, and Rom 3:22. They treat this genitive phrase as an objective genitive. But this translation does not seem to fit Paul's thought and his gospel.
In Gal 2:16, one's justification (not in the sense of imputed/imparted righteousness) means that he/she stands in a right/good relationship with God. Paul says that this right relationship with God is possible through Christ's faith (pistis christou). It is not by "faith in Jesus." In other words, if one lives by Christ's faith, he/she is in a good relationship with God. That is what justification (dikaiosyne) means by Paul. The similar idea of this is also found in Rom 1:17 (c.f., Hab 2:4): "The righteous one shall live by faith."
This righteous relationship with God is not by particular law, works, or any tradition, but through living in Christ or following his faith. In this light, justification is not made once and for all. It must be sought and lived out until the end.
With this above understanding, Gal 2:16 is translated as follows: "yet we know that a person is justified not by (from) the works of the law but through Jesus Christ's faithfulness. And we have come to trust Christ Jesus, so that we might be justified by Christ's faith, and not by doing the works of the law because no one will be justified by the works of the law."
ἐξ ἔργων νόμου ἐὰν μὴ διὰ πίστεως Ἰησοῦ Χριστοῦ,
The importance of Jesus Christ's faith is further emphasized in Gal 2:20 in which Paul says that he wants to live by Jesus Christ's faith. This verse is also translated as follows: "and it is no longer I who live, but it is Christ who lives in me. And the life I now live in the flesh I live by the faith of the Son of God, who loved me and gave himself for me."
Pistis christou is also important in Rom 3:22, in which Paul summarizes his threefold gospel: God's righteousness, Christ's faith, and Christian participation in his faith.
Translation issues in Rom 3:21-26 and Gal 2:20
New Revised Standard Version:
21 But now, apart from law, the righteousness of God has been disclosed, and is attested by the law and the prophets, 22 the righteousness of God through faith in Jesus Christ for all who believe. For there is no distinction, 23 since all have sinned and fall short of the glory of God; 24 they are now justified by his grace as a gift, through the redemption that is in Christ Jesus, 25 whom God put forward as a sacrifice of atonement by his blood, effective through faith. He did this to show his righteousness, because in his divine forbearance he had passed over the sins previously committed; 26 it was to prove at the present time that he himself is righteous and that he justifies the one who has faith in Jesus.
The most neutral translation of a genitive case phrase is to provide "of" between the head noun and the substantive. That is, when we translate dikaiosyne (righteousness) theou (of God), we can translate it as "the righteousness of God." By this English readers may know this is a genitive phrase, which must be carefully interpreted. We find this kind of "of" combined genitive in English Bibles: for example, the body of Christ, the love of God, the body of sin, the blasphemy of the Spirit, the sin of the world, and etc. In each case of a genitive, we have to say which genitive meaning is meant. Sometimes, the use of a genitive is obvious in a sentence: "Who shall separate us from the 'love of Christ'? (Rom 8:35). Here the "love of Christ" means Christ's love (not your love for Christ); so this is a subjective genitive meaning. Now when it comes to "pistis christou" (the faith of Christ), another Greek genitive, the NRSV didn't follow the neutral policy of translation as it did with "the righteousness of God." Instead, the NRSV translated it as an objective genitive: "faith in Christ" (see 3:22 and 26). This is a problem of inconsistency about the translation. In order to be consistent, the NRSV should have translated "pistis christou" as "faith of Christ," whose genitive meaning needs interpretation. I am certain that both of these genitive phrases mean the subjective sense: God's righteousness and Christ's faithfulness. Among many evidence that I may find from Paul's undisputed letters, the most decisive evidence is this: If Paul had intended "faith in Christ" in the above passage, he could have used the prepositional phrase with "en": "pistis en christo" instead of the genitive case because "pistis en christo" clearly conveys believer's faith in Christ. But Paul used a genitive phrase in Romans and elsewhere in the undisputed letters. Therefore, we can safely say that here the genitive "pistis christou" must mean Christ's faithfulness. Actually, if we read Romans as a whole (or Galatians), we can further feel confident that Paul means a subjective meaning of Christ's faithfulness through which God's righteousness is revealed for all who have Christ's faith. You may wonder then why the NRSV is inconsistent in its translation of a genitive.
Common English Bible:
21 But now God’s righteousness has been revealed apart from the Law, which is confirmed by the Law and the Prophets. 22 God’s righteousness comes through the faithfulness of Jesus Christ for all who have faith in him. There’s no distinction. 23 All have sinned and fall short of God’s glory, 24 but all are treated as righteous freely by his grace because of a ransom that was paid by Christ Jesus. 25 Through his faithfulness, God displayed Jesus as the place of sacrifice where mercy is found by means of his blood. He did this to demonstrate his righteousness in passing over sins that happened before, 26 during the time of God’s patient tolerance. He also did this to demonstrate that he is righteous in the present time, and to treat the one who has faith in Jesus as righteous.
Now compare NRSV with CEB. The immediately noticeable things are clear; CEB translates "dikaiosyne theou" as "God's righteousness" which is a subjective genitive. Likewise, "pistis christou" as "the faithfulness of Jesus" which is a subjective genitive meaning (Jesus' faithfulness). Yet CEB is also inconsistent in its translation; for example, "faith in him" (v.22) is an interpretation of "those who believe." There is no "in him" in Greek. More surprisingly, "faith in Jesus" (v.26) is also an interpretation of the genitive "pistis christou," which can be a meaning of either subjective or objective genitive. In order to be consistent, the CEB could translate like this: "the one who has the faithfulness of Jesus." In the end, what it did in verse 26 is to confirm the doctrine of justification by faith: "to treat the one who has faith in Jesus as righteous." Rather, the plain meaning of this is: "God justifies the one who has the faithfulness of Jesus" which is coherent with "pistis christou" in v.22.
New International Version (old version):
21 But now a righteousness from God, apart from law, has been made known, to which the Law and the Prophets testify. 22 This righteousness from God comes through faith in Jesus Christ to all who believe. There is no difference, 23 for all have sinned and fall short of the glory of God, 24 and are justified freely by his grace through the redemption that came by Christ Jesus. 25 God presented him as a sacrifice of atonement, through faith in his blood. He did this to demonstrate his justice, because in his forbearance he had left the sins committed beforehand unpunished-- 26 he did it to demonstrate his justice at the present time, so as to be just and the one who justifies those who have faith in Jesus.
NIV renders the Greek genitive cases of "the righteousness of God," and "faith of Christ" as the objective meaning. It interpreted for readers that these genitive cases are meant to be objective meaning. I disagree! Paul's gospel is not about "how I am saved" but about "how we become children of God." What you see here in this translation is an imputed or imparted righteousness to believers. It is like God having lots of righteousness and distributing to believers once and for all. This is a forensic salvation perspective or old perspective on Paul. Again, I don't think Paul is concerned about the Western-view of an individualistic justification. He is a thorough community person. He says in Rom 9:2-4: "I have great sorrow and unceasing anguish in my heart. 3 For I could wish that I myself were cursed and cut off from Christ for the sake of my brothers, those of my own race, 4 the people of Israel." His vision is the salvation of both Jews and Gentiles. Another problem is found in v.26. Why does NIV change righteousness to justice because the same Greek noun "dikaiosyne" was used here? "His justice" is chosen here to evoke the satisfaction theory of atonement in which God's moral justice is satisfied by Christ's sinless death. That is something we don't see in the text though it is not impossible to read that way. Likewise, God is "just" instead of "righteous." "Pistis christou" is also interpreted as "faith in Christ" throughout.
Galatians 2:20:
New Revised Standard Version:
20 and it is no longer I who live, but it is Christ who lives in me. And the life I now live in the flesh I live by faith in the Son of God, who loved me and gave himself for me.
"en pistei zo te tou hioue tou theou" in Greek means "I live in the faith of the Son of God" (genitive phrase). Paul simply says here: "I live in Jesus' faith" if this means a subjective genitive. Paul says now Christ lives in him, and therefore, he lives with Christ's faith. That is the most natural flow of meaning. But NRSV takes this as an objective genitive meaning, so making Paul put his faith in Jesus. This is very awkward.
Common English Bible:
20 I have been crucified with Christ and I no longer live, but Christ lives in me. And the life that I now live in my body, I live by faith, indeed, by the faithfulness of God’s Son, who loved me and gave himself for me.
CEB does a great job in this verse because it clearly designates faith here as Jesus' faith.
For more about the above, see my book, A Theological Introduction to Paul's Letters.