The relative Cuntz-Pimsner algebra of a groupoid correspondence is the groupoid C*-algebra of a new groupoid with an explicit description and universal property for actions on topological spaces.
Higgins,Techniques of semigroup theory, Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 1992
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Groupoid models for relative Cuntz-Pimsner algebras of groupoid correspondences
The relative Cuntz-Pimsner algebra of a groupoid correspondence is the groupoid C*-algebra of a new groupoid with an explicit description and universal property for actions on topological spaces.