The index of operators on foliated bundles

We compute the equivariant cohomology Chern character of the index of elliptic operators along the leaves of the foliation of a flat bundle. The proof is based on the study of certain algebras of pseudodifferential operators and uses techniques for analizing noncommutative algebras similar to those developed in Algebraic Topology, but in the framework of cyclic cohomology and noncommutative geometry.