  Let G be a compact, simply connected Lie group. We develop a `quantization
functor' from pre-quantized quasi-Hamiltonian G-spaces at level k to the fusion
ring (Verlinde algebra) R_k(G). The quantization Q(M) 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.
