Elliptic boundary value problems associated with isometric group actions (Q2244734)

The authors consider the index problem in nonlocal elliptic boundary value problems and associated with isometric actions of discrete groups on some suitable manifolds. Let us describe a few sections of the article. In the second section the authors recall definitions related to the Boutet de Monvel algebra of pseudodifferential boundary value problems on a manifold with boundary. The third section focuses on the study of the algebra generated by Boutet de Monvel operators and shift operators associated with isometric actions of discrete groups of polynomial growth on manifolds with boundary. The fourth section deals with the construction of cohomology of de Rham-type for manifolds whose boundary is the total space of a fibration. In the fifth section section, they introduce noncommutative differential forms on the boundary and regularized traces on them. In the sixth section, they provide the definition of the Todd class of the manifold and state the index theorem where the proof is furnished in the seventh and the eighth sections.