EQUIVARIANT K-THEORY AND THE CHERN CHARACTER FOR DISCRETE GROUPS

Let X be a compact Hausdorff space, let Gamma be a discrete group that acts continuously on X from the right, define (X) over tilde = {(x, gamma) is an element of X x Gamma : x center dot gamma = x}, and let Gamma act on (X) over tilde via the formula (x, gamma) center dot alpha = (x center dot alpha, alpha(-1)gamma alpha). Results of P. Baum and A. Connes, along with facts about the Chern character, imply that K-Gamma(i)(X) and K-i((X) over tilde/Gamma) are isomorphic up to torsion for i = 0, 1. In this paper, we present an example where the groups K-Gamma(i)(X) and K-i((X) over tilde/Gamma) are not isomorphic.