Farrell-Jones Conjecture for finite groups (Ex)

Let $G$$<wikitex>; Let $G$ be a finite group. Show that the assembly map $$ H_0(BG;{\bf\mathrm{K}}_{\C}) \xrightarrow{} K_0(\C G) $$ is bijective if and only if $G$ is trivial. (Use the fact that $K_n(\C)$ vanishes for $n \le -1$ and is infinite cyclic for $n = 0$.) </wikitex> [[Category:Exercises]] [[Category:Exercises without solution]]G$ be a finite group. Show that the assembly map

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$$\displaystyle H_0(BG;{\bf\mathrm{K}}_{\C}) \xrightarrow{} K_0(\C G)$$

is bijective if and only if $G$$G$ is trivial. (Use the fact that $K_n(\C)$$K_n(\C)$ vanishes for $n \le -1$$n \le -1$ and is infinite cyclic for $n = 0$$n = 0$.)