There is Rosenberg-Schochet universal coefficient theorem, which says $KK(A,B)\simeq Ext(K_*(A),K_{+1}(B))\oplus Hom(K_(A),K_*(B))$ Ext(K_{\ast}(A),K_{\ast+1}(B))\oplus Hom(K_{\ast}(A),K_{\ast}(B))$(not canonically) when$A$is$KK$-equivalent to a commutative algebra. It was proved in The Künneth theorem and the universal coefficient theorem for Kasparov’s generalized K-functor, Duke Math. J., 55(1987), 431–474. 1 There is Rosenberg-Schochet universal coefficient theorem, which says$KK(A,B)\simeq Ext(K_*(A),K_{+1}(B))\oplus Hom(K_(A),K_*(B))$(not canonically) when$A$is$KK\$-equivalent to a commutative algebra. It was proved in The Künneth theorem and the universal coefficient theorem for Kasparov’s generalized K-functor, Duke Math. J., 55(1987), 431–474.