I am also eagerly waiting for Philologo's response.
Gee, I can hardly wait to see what I might say!;-)
[color=0000ff]εν πιστει ζω τη του υιου του Θεου, (Gal 2:20 GNT-TRS)[/color] The literal translation of this phrase would be something like [color=0000ff]in/by faith I live the of the Son of the God[/color] so its one of those places where an interlinear struggles to get to the real meaning. Let’s unpack it
[b]εν πιστει ζω[/b] This would give something like ‘I live by faith’ The Greek preposition ‘en’ means ‘in’ or ‘within’ but it is sometimes used ‘instrumentally’ (bet you wished you hadn’t asked now!) When Biblical Greek want to say ‘kill with the sword’ it would use ‘en’ in the sense of ‘by the sword’; the sword being the ‘instrument’ of the killing. We have to take note of the context to see which is most appropriate. In this instance my judgement would be that it means ‘by faith’. It should be noted that there is no definite article here and those Cambridge Bibles that we have been hearing about should have put the word ‘the’ into italics so that it read [color=0000ff]“I now live in [i]the[/i] flesh” (Gal 2:20 KJVS)[/color] More modern versions have sometimes corrected this eg [color=0000ff]“I now live in the flesh I live in faith” (Gal 2:20 ASV)
“I live by faith” (Gal 2:20 NKJV)[/color]So it is not ‘the faith’ of the Son of God but ‘faith’.
Next we have the bit τη του υιου του Θεου where
[b]τη[/b] is ‘the definite article’ and is Dative, Singular, Feminine. It is referring backwards to the feminine gender word ‘faith’. I think it could best be translated as ‘that’. So that the sentence now reads “I live by faith, that (faith)”
[b]του υιου[/b] is the definite article and is Genitive, Singular, Masculine followed by the word ‘son’. This is the Greek way of saying ‘belonging to the son’.
[b]του Θεου[/b] the definite article and is Genitive, Singular, Masculine followed by the word ‘God’. This is the Greek way of saying ‘belonging to God’.
So we have a reference to God’s Son’s faith. The question then is does this mean ‘faith in him’ or ‘faith from him’? I think it means the kind of faith that he had, which was the faith of a son. In Roman’s Paul refers to Abraham’s faith[color=0000ff]“And the father of circumcision to them who are not of the circumcision only, but who also walk in the steps of that faith of our father Abraham, which he had being yet uncircumcised.” (Rom 4:12 KJVS)[/color] Again the word 'faith' is without the definite article. It is literally ‘in the steps of our father Abraham’s faith’; this is the same kind of construction as Galatians 2:20.
It is referring to ‘Abrahamic faith’, the kind of faith that Abraham had; we sometimes call this 'justifying faith'. Jews had to have both circumcision AND Abrahamic faith. The point I am making is that Abraham did not give them this faith, it was faith like Abraham's. If we carry through this idea of a ‘kind of faith’ into Galatians it seems that Paul is referring to the ‘kind of faith’ that the Son had. This would be significant because Paul later goes on to point out that ‘faith’ has now arrived (Gal 3:25) and is part of the way in which we become ‘sons’ of God, God giving us the Spirit of his Son.
John Wesley was questioned about his claims that before his ‘warm heart’ experience he did not have ‘faith’. His questioners reminded him that he was Anglican priest and had been a missionary to the American colonies. His answer was that the faith he had then was the faith of a slave not that of a son.
I don’t think Galatians 2:20 is talking about Christ’s own personal faith being given to us, but of Paul’s experience of a Son-like faith. Slaves obeyed God because they had to; sons because they chose to. Slaves were kept in check by a law; sons walk in the Spirit. Personally I would rather take both broad interpretations than an either/or choice. This is Christwards and Sonlike faith, but it is not, I think, Christ’ faith instead of Paul’s faith.