A Split Exact Sequence of Equivariant K-groups of Virtually Nilpotentt Groups

Let be an extension of a torsion free nilpotent group by a finite group G, of odd order. Then admits a cocompact proper action on ⁿ. This action determines an action of G on a nil-manifold by isometries. In this paper, the equivariant K-theory of the finite group action is studied and it is shown that the forget control map is a split monomorphism.