Weinberger–Yu conjecture for finite-part independence in reduced operator K-theory

Let $G$ be a group with torsion elements $g_1,g_2,\ldots,g_k$ of distinct positive orders $d_1,\ldots,d_k$. For each $g_i$, let $p_i$ be the idempotent corresponding to $g_i$, and let $EG$ be the universal space for proper and free $G$-action. Reduced finite-part conjecture. The elements $1,p_1,\ldots,p_k$ are linearly independent in K_0(C^*_{\red}G). Moreover, every nonzero element of the subgroup generated by $p_1,\ldots,p_k$ lies outside the image of the assembly map

$$K^G_0(EG)\longrightarrow K_0(C^*_{\max}(G)).$$

This is proposed as the reduced-algebra analogue of the Weinberger–Yu conjecture. The paper establishes the relevant trace-detection criterion for rapid-decay groups and proves the maximal conjecture in several classes, but does not resolve this reduced statement in general.