Varghese, M.Zhang, W.2010-10-192010-10-192010Advances in Mathematics, 2010; 225(3):1224-12470001-87081090-2082http://hdl.handle.net/2440/61336We first introduce an invariant index for G-equivariant elliptic differential operators on a locally compact manifold M admitting a proper cocompact action of a locally compact group G. It generalizes the Kawasaki index for orbifolds to the case of proper cocompact actions. Our invariant index is used to show that an analog of the Guillemin-Sternberg geometric quantization conjecture holds if M is symplectic with a Hamiltonian action of G that is proper and cocompact. This essentially solves a conjecture of Hochs and Landsman. © 2010 Elsevier Inc.enCopyright 2010 Elsevier Inc. All rights reserved.Geometric quantizationLocally compact groupsHochs–Landsman conjectureGuillemin–Sternberg conjectureEquivariant K-theoryIndex theorem for generalized orbifoldsJournal article002009665810.1016/j.aim.2010.03.0230002810457000042-s2.0-7795584470334919Varghese, M. [0000-0002-1100-3595]