$C^*$-algebras of $b$-pseudodifferential operators and an   $\R^k$-equivariant index theorem
  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. 
Richard B. Melrose and Victor Nistor