Let $ G $ be a second countable locally compact group.
Let $ A $ and $ B $ be two $G$-$C^*$-algebras.
Let $ KK^G (A, B) $ be the $G$-equivariant $KK$-theory of the pair $ (A, B) $.
Could you tell me please, when $ KK^G (A, B) $ is a free $ \mathrm{Rep}(G) $-module of finite rank ?
$ \mathrm{Rep}(G) $ is the representation ring of $ G $.
Thanks in advance for your help.