I suggest if we look at the context of Galatians, it's people adding circumcision and works of the old law to the law of Christ. Although Paul is a Jew and circumcised, he counts it as rubbish and only boasts in the law of Christ (cross). We either follow the flesh or we follow Christ.Paul says he boasts in the Cross of Christ alone (instead of in his Jewishness, etc)--he doesn't mean the wood, he means "the righteous deeds of Christ, and the benefit that affords me".
It's about our works.
5:16 But I say, walk by the Spirit, and you will not gratify the desires of the flesh. [/quote]
6:2 Bear one another's burdens, and so fulfill the law of Christ. [/quote]
I don't see how we can squeeze Jesus's righteous deeds in there. It's about our walk.