Recently, Balmer—Gallauer deduced the tensor-triangular geometry of the so-called "derived category of permutation modules," which controls both the usual modular representation theory of a finite group as well as that of its "p-local" subgroups. Their construction of "permutation twisted cohomology" plays a key role in their deduction in the case of elementary abelian $p$-groups; here the authors deduce far stronger geometric results. In this talk, after reviewing some basics about tensor-triangular geometry and permutation modules, we'll describe how one can utilize endotrivial complexes, the invertible objects of this category, to extend Balmer—Gallauer's results for elementary abelian $p$-groups to all $p$-groups.