The L-theory Farrell–Jones conjecture for torsionfree groups

Let $G$ be a group, let $R$ be a ring with involution, and let $\mathbf{L}^{\langle-\infty\rangle}(R)$ be the associated $L$-theory spectrum, whose $n$th homotopy group is $L_n^{\langle-\infty\rangle}(R)$. The L-theory Farrell–Jones conjecture. If $G$ is torsionfree, then the assembly map

$$H_n(BG;\mathbf{L}^{\langle-\infty\rangle}(R))\longrightarrow L_n^{\langle-\infty\rangle}(RG)$$

is an isomorphism for every $n\in\mathbb{Z}$. This is the $L$-theoretic counterpart of the algebraic $K$-theory Farrell–Jones conjecture; the source gives no resolution status.