Surgery and the relative index in elliptic theory.

Nazaikinskii, V.E.; Sternin, B.Yu.

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We consider a class of nonlocal operators associated with an action of a compact Lie group G on a smooth closed manifold. Ellipticity condition and Fredholm property for elliptic operators are obtained. This class of operators is studied using pseudodifferential uniformization, which reduces the problem to a pseudodifferential operator acting in sections of infinite-dimensional bundles.