The algebraic K-theory Farrell–Jones conjecture for torsionfree groups

Let $G$ be a group, let $R$ be a regular ring, and let $BG$ be a classifying space for $G$. The spectrum $\mathbf{K}(R)$ represents algebraic $K$-theory, and the assembly map is the canonical map from the homology of $BG$ with these coefficients to the $K$-theory of the group ring. The algebraic K-theory Farrell–Jones conjecture. If $G$ is torsionfree, then

$$H_n(BG;\mathbf{K}(R))\longrightarrow K_n(RG)$$

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