Elliptic Theory and Noncommutative Geometry pp 127-136 | Cite as

# Index of Nonlocal Operators over *C**-Algebras

## Abstract

In this chapter, we obtain index formulas for nonlocal elliptic operators **D** = (*D, P*_{1}, *P*_{2}) over some *C**-algebra Λ.^{1} As in the Mishchenko-Fomenko index theory [57], where one considers the index of local elliptic operators over *C**-algebras and whose ideology we follow to a large extent here, the main role in the structure and the proof of such index formulas is played by the Künneth formula describing the *K*-group of tensor products of *C**-algebras. To ensure that the Künneth formula applies, we assume throughout the chapter that the algebra Λ belongs to the so-called class *N* (*bootstrap class*) in the sense of [66]. Let us recall the definition of this class.

## Keywords

Tensor Product Exact Sequence Projective Module Topological Index Index Theorem## Preview

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