Finite group actions and elliptic genera

We study the modular properties of a formal power series of elliptic operators that correspond to the S(sup 1)-equivariant index of a hypothetical Dirac operator on loop spaces of a manifold twisted by the action of a group. We also show that this interpretation leads to a natural construction of Virasoro equivariant vector bundles over the loop space of points fixed under the action of the group.