For a topological groupoid $G$, there are two kinds of ``topological'' $K$-homology theories, $K_{\ast}^{G}(\underline{EG})$ the $K$-homology of $G$ with $G$-compact support, and $K_{\ast}(BG)$ the topological $K$-homology of the classifying space of $G$.

In the introduction of this paper, Baum, Connes, and Higson stated that $K_{\ast}^{G}(\underline{EG})$ is isomorphic to $K_*(BG)$ when $G$ is a torsion-free discrete group. I wonder

What happens to other cases? Especially when $G$ is a topological groupoid?