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We interpret certain equivariant Kasparov groups as equivariant representable K‐theory groups and compute these via a classifying space and as K‐theory groups of suitable σ‐ C  * ‐algebras. We also relate equivariant vector bundles to these σ‐ C  * ‐algebras and provide sufficient conditions for equivariant vector bundles to generate representable K‐theory. We mostly work in the generality of locally compact groupoids with Haar systems.

Equivariant representable K‐theory