The rationalized Farrell-Jones conjecture

Let $G$ be a group and $n\in\mathbb{Z}$. The rationalized Farrell-Jones assembly map is

$$\bigoplus_{(C)\in(\mathcal{FCyc})}\ \bigoplus_{\substack{s+t=n\s\geq0,\,t\geq-1}} H_s(BZ_GC;\mathbb{Q})\otimes_{\mathbb{Q}[W_GC]}\Theta_C\bigl(K_t(\mathbb{Z}[C])\otimes_{\mathbb{Z}}\mathbb{Q}\bigr)\longrightarrow K_n(\mathbb{Z}[G])\otimes_{\mathbb{Z}}\mathbb{Q},$$

where $(C)$ ranges over conjugacy classes of finite cyclic subgroups, $Z_GC$ is the centralizer, $W_GC$ is the Weyl group, and $\Theta_C$ is the specified idempotent endomorphism.

Rationalized Farrell-Jones conjecture. For every group $G$ and every $n\in\mathbb{Z}$, this rationalized Farrell-Jones assembly map is an isomorphism.

This is the rationalized version of the Farrell-Jones conjecture and extends Hsiang's conjecture from torsion-free groups to arbitrary groups.