For any C*-correspondence with a generalized gauge action by a locally compact Hausdorff group, the Cuntz-Pimsner algebra of the reduced crossed product is canonically isomorphic to the reduced crossed product of the Cuntz-Pimsner algebra.
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The Hao-Ng isomorphism theorem for reduced crossed products
For any C*-correspondence with a generalized gauge action by a locally compact Hausdorff group, the Cuntz-Pimsner algebra of the reduced crossed product is canonically isomorphic to the reduced crossed product of the Cuntz-Pimsner algebra.