  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.
