The study demonstrates quasi-invariant lifts of completely positive maps in a groupoid framework, suggesting new pathways in C*-algebra theory.
Let G be a locally compact, Hausdorff, second countable groupoid and A be a separable, C₀(G⁽⁰⁾) -nuclear, G - C^* -algebra. We prove the existence of quasi-invariant, completely positive and contractive lifts for equivariant, completely positive and contractive maps from A into a separable, quotient C^* -algebra. Along the way, we construct the Busby invariant for G -actions.
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Bhattacharjee et al. (2025) studied this question.
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