$C^*$-algebras of $b$-pseudodifferential operators and an $\R^k$-equivariant index theorem

Abstract

We compute $K$-theory invariants of algebras of pseudodifferential operators on manifolds with corners and prove an equivariant index theorem for operators invariant with respect to an action of $\R^k.$ We discuss the relation between our results and the $\eta$-invariant.