CUNTZ-PIMSNER C*-ALGEBRAS AND CROSSED PRODUCTS BY HILBERT C*-BIMODULES

Given a correspondence X over a C*-algebra A, we construct a C*-algebra A(infinity)(X) and a Hilbert C*-bimodule X(infinity) over A(infinity)(X) such that the augmented Cuntz-Pimsner C*algebras (O) over tilde (X) and the crossed product A(infinity)(X) (sic) X(infinity)(X) are isomorphic. This construction enables us to establish a condition for two augmented Cuntz-Pimsner C*-algebras to be Morita equivalent.