The complex bordism of groups with periodic cohomology

Abstract

Is is proved that if B G BG is the classifying space of a group G G with periodic cohomology, then the complex bordism groups M U ∗ ( B G ) M{U_{\ast }}(BG) are obtained from the connective K K -theory groups k u ∗ ( B G ) k{u_{\ast }}(BG) by just tensoring up with the generators of M U ∗ M{U_{\ast }} as a polynomial algebra over k u ∗ k{u_{\ast }} . The explicit abelian group structure is also given. The bulk of the work is the verification when G G is a generalized quaternionic group.