On the index of noncommutative elliptic operators over C*-algebras

We consider noncommutative elliptic operators over C*-algebras, associated with a discrete group of isometrics of a manifold. The main result of the paper is a formula expressing the Chern characters of the index (Connes invariants) in topological terms. As a corollary to this formula a simple proof of higher index formulae for noncommutative elliptic operators is obtained.