Geodesic
On the index of noncommutative elliptic operators over $C^*$-algebras
Sbornik. Mathematics, Tome 201 (2010) no. 3, pp. 377-417

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider noncommutative elliptic operators over $C^*$-algebras, associated with a discrete group of isometries 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. Bibliography: 36 titles.
Keywords: noncommutative elliptic operators, operators over $C^*$-algebras, index formulas, crossed product. 
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A. Yu. Savin; B. Yu. Sternin. On the index of noncommutative elliptic operators over $C^*$-algebras. Sbornik. Mathematics, Tome 201 (2010) no. 3, pp. 377-417. http://geodesic.mathdoc.fr/item/SM_2010_201_3_a3/