Let $Wh_0(G) ={K_0(\mathbb Z[G])}/{\mathbb Z}$, where $\mathbb Z[G]$ is the group ring of $G$ over $\mathbb Z$. Weibel states that the augmentation map $f: \mathbb Z[G] \to \mathbb Z$ induces the decomposition $K_0(\mathbb Z[G])\cong \mathbb Z \oplus Wh_0(G)$.
I see that the map induces a map $g: K_0(\mathbb Z[G]) \to K_0(\mathbb Z) = \mathbb Z$. But I can't quite write down the short exact sequence he has in mind. What would it be?