Geodesic
The equivariant index of $C^*$-elliptic operators
Izvestiya. Mathematics , Tome 29 (1987) no. 1, pp. 207-224.

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Let $G$ be a compact Lie group, and $A$ a $C^*$-algebra with identity. A $K$-theory of $G$-equivariant $A$-vector bundles is developed along with a corresponding theory of Fredholm operators, and the analytic and topological indices of an elliptic equivariant pseudodifferential operator over a $C^*$-algebra $A$ are defined. An index theorem generalizing the Mishchenko–Fomenko theorem is proved. Bibliography: 19 titles. 
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E. V. Troitskii. The equivariant index of $C^*$-elliptic operators. Izvestiya. Mathematics , Tome 29 (1987) no. 1, pp. 207-224. http://geodesic.mathdoc.fr/item/IM2_1987_29_1_a11/

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