Equivariant K-theory and forms over twisted group rings

Abstract

Let X be a topological space equipped with the action of a finite group ∏. We may form the twisted group ring of ∏, coefficients being elements of the ring of continuous functions on X with values in the real numbers, complex numbers or quaternions. In this paper we show how the Witt groups of hermitian forms of various kinds over these twisted group rings can be described in terms of the real, complex or quaternionic equivariant K-theory of X.