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Let  G  be a compact, simply connected Lie group. We develop a ‘quantization functor’ from prequantized quasi-Hamiltonian  G -spaces ( M , ω , Φ ) at level  k  to the fusion ring (Verlinde algebra)  R   k  ( G ). The quantizationis 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 calculatein several examples.

Twisted K -Homology and Group-Valued Moment Maps