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