Meta-Isomorphism Conjecture for spectra

Let $G$ be a group, let ${\mathbf E}^G:\operatorname{Or}(G)\to\operatorname{Spectra}$ be a covariant functor, let $\mathcal{F}$ be a family of subgroups of $G$, and let $E_{\mathcal{F}}(G)$ be a model for the corresponding classifying space. The projection $\operatorname{pr}:E_{\mathcal{F}}(G)\to G/G$ induces a map of the associated homology spectra.

Meta-Isomorphism Conjecture. The induced map

$$({\mathbf E}^G)_{\%}(\operatorname{pr}):({\mathbf E}^G)_{\%}(E_{\mathcal{F}}(G))\to({\mathbf E}^G)_{\%}(G/G)={\mathbf E}^G(G/G)$$

is a weak homotopy equivalence. This is the spectrum-level form of the assembly conjecture and specializes to major isomorphism conjectures by choosing ${\mathbf E}^G$ and $\mathcal{F}$.