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Oct 12, 2018 at 12:57 vote accept S. carmeli
Oct 12, 2018 at 12:48 comment added S. carmeli @Neil Strickland Thanks, Ill look. I guess the hard part of the KU-Milnor conjecture should be to show that the K-theory of G as a discrete group is topologically generated by representation classes.
Oct 11, 2018 at 21:12 comment added skd @S.carmeli Check out the Atiyah-Segal theorem, which tells you what happens when G is compact Lie.
Oct 9, 2018 at 18:48 comment added S. carmeli Thanks for the observation. I will add this to the question if you don't mind, because it makes it much more natural to ask. For a Lie group, you know what is the precise relationship between $K_1^*BG$ and the representations of $G$? for a finite group I know that $KU$-cohomology is the completion of the representation ring, but for a Lie group or for its completion I don't know what is the relation.
Oct 9, 2018 at 9:24 history answered Neil Strickland CC BY-SA 4.0