A Lorentzian Equivariant Index Theorem

We develop an equivariant index theorem for a twisted Dirac operator on a compact globally hyperbolic spacetime with spacelike boundary on which a group acts isometrically, subject to the Atiyah-Patodi-Singer boundary condition. Our analysis shows that the geometric 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 a boundary contribution. Our proof is based on spectral flow and the key observation that the equivariant spectral flow can be obtained from the standard spectral flow. (Joint work with L. Ronge based on arXiv:2602.16547 [math.DG]).