A note on the equivariantDold–Thom theorem

In this note we prove a version of the classical Dold–Thom theorem for the RO(G)-graded equivariant homology functors , where G is a finite group, M is a discrete -module, and is the Mackey functor associated to M. In the case where with the trivial G-action, our result says that, for a G-CW-complex X, and for a finite dimensional G-representation V, there is a natural isomorphism where denotes the free abelian group on X.