Countable stratification conjecture for equivariant bootstrap categories

Let $G$ be a finite group, and let $\Cell{G}$ denote the equivariant bootstrap subcategory of $G$-C*-algebras. A category is countably stratified when its localizing tensor ideal subcategories—understood as triangulated subcategories closed under countable coproducts—are classified by countable Balmer--Favi supports via the analogue of the usual support-theoretic bijection.

Countable stratification conjecture. The category $\Cell{G}$ is countably stratified for every finite group $G$.

The paper proves countable stratification when every nontrivial element of $G$ has prime order, including groups such as $S_3$, $A_5$, and $p$-groups of exponent $p$. The conjecture extends this result to all finite groups.