The complex Bass conjecture

Let $G$ be a discrete group, and let

$$HS:K_0(C{C}G)\longrightarrow\bigoplus_{[G]}C{C}$$

be the Hattori–Stallings trace, where $[G]$ denotes the set of conjugacy classes of elements of $G$. The $C{C}G$ Bass conjecture. The image of $HS$ is contained in the $C{C}$-vector space spanned by conjugacy classes of elements of finite order. Linnell's result gives the vanishing for finite-order nonidentity elements in the relevant integral setting; the broader formulation is presented as a version of the Bass conjecture and is not resolved in the supplied text.