We express the index of the SpinC-Dirac operator on symplectic quotients of a Hamiltonian loop group manifold in terms of fixed point data. As an application we prove Verlinde formulas for the SpinC-quantization of moduli spaces of flat bundles over surfaces.
"The Verlinde formula as fixed point formulas." J. Symplectic Geom. 1 (1) 1 - 46, December, 2001.