The compact-open Farrell–Jones conjecture for Hecke categories

Let $G$ be a td-group and let $\mathcal{B}$ be a Hecke category with $G$-support satisfying condition (Reg): for every natural number $d$ there is a natural number $l(d)$ such that, for every compact open subgroup $U\subseteq G$, the additive category $\mathcal{B}[G/U]_{\oplus}[\mathbb{Z}^d]$ is $l(d)$-uniformly regular coherent. The $\mathcal{C}\mathrm{op}$-assembly map is

$$H_n^G(E_{\mathcal{C}\mathrm{op}}(G);\mathbf{K}_{\mathcal{B}})\longrightarrow H_n^G(G/G;\mathbf{K}_{\mathcal{B}})=\operatorname{K}_n(\mathcal{B}).$$

Compact-open Farrell–Jones conjecture. This assembly map is an isomorphism for all $n$. This is the paper's main assembly statement for Hecke categories under (Reg); the supplied text gives no resolution evidence.