Equivariant complex bundles, fixed points and equivariant unitary bordism

Abstract

We study the fixed points of the universal $G$–equivariant complex vector bundle of rank $n$ and obtain a decomposition formula in terms of twisted equivariant universal complex vector bundles of smaller rank. We use this decomposition to describe the fixed points of the complex equivariant K–theory spectrum and the equivariant unitary bordism groups for adjacent families of subgroups.