A note on the equivariant Dold-Thom theorem

In this note we prove a version of the classical Dold-Thorn theorem for the RO(G)-graded equivariant homology functors H-*(G) (-; M), where G is a finite group, M is a discrete Z[G]-module, and M is the Mackey functor associated to M. In the case where M=Z with the trivial G-action, our result says that, for a G-CW-complex X, and for a finite dimensional G-representation 1; there is a natural isomorphism [S-V, F-0(X)](G) congruent to H-V(G) (X; Z), where F-0(X) denotes the free abelian group on X. (C) 2003 Elsevier B.V. All tights reserved.