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 $widetilde{X} = {(x,gamma) in X times Gamma : xcdotgamma= x}$, and let $Gamma$ act on $widetilde{X}$ via the formula $(x,gamma)cdotalpha = (xcdotalpha, alpha^{-1}gammaalpha)$. Results of P. Baum and A. Connes, along with facts about the Chern character, imply that $K^i_Gamma(X) otimes mathbb{C} cong K^i(widetilde{X}slashGamma) otimes mathbb{C}$ for $i = 0, -1$. In this note, we present an example where the groups $K^i_Gamma(X)$ and $K^i(widetilde{X}slashGamma)$ are not isomorphic.