Index of nonlocal elliptic operators over C*-algebras

A study was conducted to demonstrate index of nonlocal elliptic operators over C*-algebras. The elliptic theory of pseudo-differential operators (PDOs) over C*-algebras was also constructed in the study. A nonlocal elliptic operator over C*-algebras associated with a discrete diffeomorphism group of a manifold was also considered for the study. A compact Lie group of diffeomorphisms of a compact closed connected manifold and a subgroup of polynomial growth were used in the study. The study provided a formula expressing the analytical numerical invariants of operators in topological terms. Using this formula a proof of higher index formula for nonlocal elliptic operators was derived.