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A Dirac operator on a complete manifold is Fredholm if it is invertibleoutside a compact set. Assuming a compact group to act on all relevantstructure, and the manifold to have a warped product structure outside such acompact set, we express the equivariant index of such a Dirac operator as anAtiyah-Segal-Singer type contribution from inside this compact set, and acontribution from outside this set. Consequences include equivariant versionsof the relative index theorem of Gromov and Lawson, in the case of manifoldswith warped product structures at infinity, and the Atiyah-Patodi-Singer indextheorem.

An absolute version of the Gromov-Lawson relative index theorem