ISB ~ Galatians 2 v12

separated himself:Peter reverts to the custom of traditional Judaism, which discouraged social contact, especially shared meals, between Jews and Gentiles (Acts 10:28; Jubilees 22, 16). It was feared, among other things, that Gentile food might violate the purity standards of the Torah, i.e., it might be either unclean or improperly prepared (Lev 11:1-47; 17:1013). The problem here is that Peter has already been informed that the Jewish dietary laws have been set aside in the New Covenant and that Gentiles are now welcome members of the family of faith (Acts 10:9-16, 28).

men came from James:Either a delegation sent by James or loyal associates of James who came on their own initiative. The former seems more likely, but, for the possibility of the latter, see Acts 15:24.

the circumcision party:Jewish Christians who discouraged table fellowship between Jews and Gentiles. Peter had been criticized by them on this issue once before (Acts 11:2-3).