The Index of <Emphasis Type="Italic">b</Emphasis>-Pseudodifferential Operators on Manifolds with Corners

On compact manifolds with corners of arbitrary codimension, we characterize the multi-cylindrical end (or b-type) pseudodifferential operators that are Fredholm on weighted Sobolev spaces and we compute their indices. The index formula contains the usual interior term manufactured from the local symbols of the operator and also contains boundary correction terms corresponding to eta-type invariants of the induced operators on the boundary faces.