Nonlocal elliptic problems associated with actions of discrete groups on manifolds with boundary

Abstract: Given a manifold with boundary endowed with an action of a discrete group on it, we consider the algebra of operators generated by elements in the Boutet de Monvel algebra of pseudodifferential boundary value problems and shift operators acting on functions on the manifold and its boundary. Under certain conditions on the group action, we construct a Chern character for symbols of elliptic elements in this algebra with values in a de Rham type cohomology of the fixed point manifolds and obtain an index formula in terms of this Chern character.