Bass's conjecture for fields of characteristic zero

Let $F$ be a field of characteristic zero and $G$ a group. Let $\operatorname{class}_F(G)_f$ denote the indicated $F$-vector space of finite conjugacy classes, and let $\operatorname{HS}_{FG}$ be the Hattori–Stallings homomorphism. Bass's conjecture. The map

$$\operatorname{HS}_{FG}\colon K_0(FG)\otimes_{\mathbb Z}F\longrightarrow \operatorname{class}_F(G)_f$$

is an isomorphism. This is another formulation of the Bass conjecture, relating projective modules over a group ring to class functions. The source records substantial special cases, but does not state a general resolution.