Hey

I am trying to find out how the Baum-Connes conjecture works over $GL(1)$ over local fiels.

I am just wondering if anybody knows how to get a countable many generators for in the L.H.S of the Baum-Connes conjecture over $GL(1)$:

$\mu: K_{j}^{G}(\beta G)\to K_{j}(C_{r}^{*}G)$,

where the $L.H.S.$ is the $K$-homology of the tree for $GL(1)$, and the R.H.S. is the $K$-theory group of reduce $C^{*}$-algebra of same group $G$.

Thanks a lot.