  Let G be a compact, simple and simply connected Lie group and $\A$ be an
equivariant Dixmier-Douady bundle over G. For any fixed level k, we can define
a G-C*-algebra $C_{\A^{k+h}}(G)$ as all the continuous sections of the tensor
power $\A^{k+h}$ vanishing at infinity. A deep theorem by Freed-Hopkins-Teleman
showed that the twisted K-homology $KK^{G}(C_{\A^{k+h}}(G), \C)$ is isomorphic
to the level k Verlinde ring R_{k}(G). By the construction of crossed product,
we define a C*-algebra $C^{*}(G,C_{\A^{k+h}}(G))$. We show that the K-homology
KK(C^{*}(G,C_{\A^{k+h}}(G)),\C) is isomorphic to the formal Verlinde module
$R^{-\infty}(G) \otimes_{R(G)} R_{k}(G)$, where $R^{-\infty}(G) =
Hom_{\Z}(R(G),\Z)$ is the completion of the representation ring.
