The finite-order operator K-theory conjecture for finitely embeddable groups

Let $G$ be a countable group. For an element $g\in G$ of finite order $d$, define

$$p_g=\frac{1}{d}\sum_{k=1}^{d}g^k$$

in $\mathbb{Q}G$, and let $K_0^{\mathrm{fin}}(C^*(G))$ be the subgroup of $K_0(C^*(G))$ generated by the classes $[p_g]$ for nonidentity finite-order elements. Let

$$\mu:K_0^G(EG)\longrightarrow K_0(C^*(G))$$

be the assembly map, where $EG$ is the universal space for a proper and free $G$-action. Finite-order operator K-theory conjecture. If $\{g_1,\ldots,g_n\}$ consists of nonidentity elements of $G$ with distinct finite orders, then the classes $[p_{g_1}],\ldots,[p_{g_n}]$ generate a free abelian subgroup of $K_0^{\mathrm{fin}}(C^*(G))$ of rank $n$, and every nonzero element of this subgroup lies outside the image of $\mu$. This predicts independent finite-order classes in operator K-theory that are not detected by the assembly map; the source gives no resolution of the claim.