On the index of elliptic boundary value problems associated with the isometric group action.

The index formulas are known in many geometric situations. In particular, many authors have developed the theory of the index of elliptic boundary value problems within the framework of classical boundary value problems (see the works of Atiyah and Bott, Hermander et al.), as well as within the framework of pseudo-differential boundary value problems from the Bout de Monvel algebra (the works of Bout de Monvel, Rempel and Schulze, Fedosov and others). In this paper, we construct a topological index of elliptic boundary value problems on manifolds with an edge endowed with the isometric action of a discrete group. To provide the index formula, we construct the Chern character of a symbol with values in suitable cohomology groups.
The formula for the index of elliptic boundary value problems twisted by projectors is also obtained. The report will describe the results obtained in joint work with A.Y. Savin.