Homotopy classification of elliptic problems associated with discrete group actions on manifolds with boundary
A. Yu. Savin, Boris Yu. Sternin Β· Ufimskii Matematicheskii Zhurnal Β· 2016
Given an action of a discrete group πΊ on a smooth compact manifold π with a boundary, we consider a class of operators generated by pseudodifferential operators on π and shift operators associated with the group action.For elliptic operators in this class, we obtain a classification up to stable homotopies and show that the group of stable homotopy classes of such problems is isomorphic to the πΎ-group of the crossed product of the algebra of continuous functions on the cotangent bundle over the interior of the manifold and the group πΊ acting on this algebra by automorphisms.