  In this article we prove that the $KH$-asembly map, as defined by Bartels and
L{\"u}ck, can be described in terms of the algebraic $KK$-theory of Cortinas
and Thom. The $KK$-theory description of the $KH$-assembly map is similar to
that of the Baum-Connes assembly map. In very elementary cases, methods used to
prove the Baum-Connes conjecture also apply to the $KH$-isomorphism conjecture.
