The index of elliptic operators over V-manifolds

Abstract

Let M be a compact smooth manifold and let G be a finite group acting smoothly on M. Let E and F be smooth G-equivariant complex vector bundles over M and let be a G-invariant elliptic pseudo-differential operator. Then the kernel and the cokernel of the operator P are finite-dimensional representations of G. The difference of the characters of these representations is an element of the representation ring R(G) of G and is called the G-index of the operator P.