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Given two correspondences X and Y, we show that (under mild hypotheses) theCuntz-Pimsner algebra of the tensor product of X and Y embeds as a certainsubalgebra of the tensor product of the Cuntz-Pimsner algebra of X and theCuntz=Pimsner algebra of Y. Furthermore, this subalgebra can be described in anatural way in terms of the gauge actions on the Cuntz-Pimsner algebras. Weexplore implications for graph algebras, crossed products by the integers, andcrossed products by completely positive maps. We also give a new proof of aresult of Kaliszewski and Quigg related to coactions on correspondences.

Cuntz-Pimsner Algebras Associated to Tensor Products of Correspondences