  Let G be a discrete group and let X be a G-finite, proper G-CW-complex. We
prove that Kasparov's equivariant K-homology groups KK^G(C_0(X),\C) are
isomorphic to the geometric equivariant K-homology groups of X that are
obtained by making the geometric K-homology theory of Baum and Douglas
equivariant in the natural way. This reconciles the original and current
formulations of the Baum-Connes conjecture for discrete groups.
