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We develop a formula for the equivariant index of a twisted Dirac operator on a compact globally hyperbolic spacetime with timelike boundary on which a group acts isometrically, subject to APS boundary conditions. The formula is the same as in the Riemannian case: the equivariant index for a group element is an integral over the fixed point set of that element plus some boundary terms. The proof uses a surprisingly simple technique for reducing from the equivariant to the non-equivariant regime in order to show an equivariant version of the Lorentzian "index = spectral flow" formula.

Related project(s):
37Boundary value problems and index theory on Riemannian and Lorentzian manifolds