On an intermediate bivariant theory for $C^*$-algebras, I
@inproceedings{Dumitracscu2002OnAI, title={On an intermediate bivariant theory for \$C^*\$-algebras, I}, author={Constantin Dorin Dumitracscu}, year={2002} }
We construct a new bivariant theory, that we call $KE$-theory, which is intermediate between the $KK$-theory of G. G. Kasparov, and the $E$-theory of A. Connes and N. Higson. For each pair of separable graded $C^*$-algebras $A$ and $B$, acted upon by a locally compact $\sigma$-compact group $G$, we define an abelian group $KE_G(A,B)$. We show that there is an associative product $KE_G(A,D) \otimes KE_G(D,B) \to KE_G(A,B)$. Various functoriality properties of the $KE$-theory groups and of the…