Harris–Viehmann conjecture for cohomology of unramified Rapoport–Zink spaces

Let $G$ be a connected, quasisplit reductive group over $4p$, let $4mu$ be a dominant cocharacter, and let $b\in \mathbf{B}(G,\mu)$. Let $M_b\subset M_S\subset G$ be standard rational Levi subgroups, and let $b'$ and $b_S$ be the associated elements. Write $H^{\bullet}(G,b,\mu)$ for the cohomological construction attached to $(G,b,\mu)$, viewed in the Grothendieck group of representations of $G(\mathbb{Q}_p)\times W_{E_{\{\mu\}_G}}$. Harris–Viehmann conjecture. One has

$$H^{\bullet}(G, b, \mu )=\sum\limits_{ (M_S, \mu_S) \in \mathcal{I}^{G, \mu}_{M_S, b_S}} (\mathrm{Ind}^G_{P_S} H^{\bullet}(M_S, b_S, \mu_S))\otimes [1][|\cdot|^{\langle \rho_G, \mu_S \rangle - \langle \rho_G, \mu \rangle}].$$

Here parabolic induction modifies only the $\operatorname{Groth}(G(\mathbb{Q}_p))$ component. This is the Harris–Viehmann formula expressing the cohomology for a non-basic local Shimura datum in terms of cohomology for Levi subgroups; the source states that a proof was expected in forthcoming work of Scholze.