Is there a simple characterisation of all rings which appear as $K_0$ of finite groups? By $K_0$ of a finite group $G$ I mean $K_0(\mathbb C[G])$ which in the same as a ring of virtual characters of finite G as far as I understand.
So they must be finitely generated free abelian groups and carry [$\lambda$-structure][1]. But what else?


  [1]: https://en.wikipedia.org/wiki/%CE%9B-ring