On a class of nonlocal elliptic operators for compact Lie groups. Uniformization and finiteness theorem

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. © 2011 Versita Warsaw and Springer-Verlag Wien.