Twisted K-Homology and Group-Valued Moment Maps

Let G be a compact, simply connected Lie group. We develop a 'quantization functor' from prequantized quasi-Hamiltonian G-spaces (M,omega,Phi) at level k to the fusion ring (Verlinde algebra) R-k(G). The quantization Q(M) epsilon R-k(G) is defined as a push-forward in twisted equivariant K-homology. It may be computed by a fixed point formula, similar to the equivariant index theorem for Spin(c)-Dirac operators. Using the formula, we calculate Q(M) in several examples.