Abstract: Let $G$ be a finite group and $R$ a commutative ring. An endotrivial complex is an invertible object in the derived category of permutation $RG$-modules, i.e., an invertible bounded chain complex of summands of permutation $RG$-modules. Previously, we classified the endotrivials for all groups when $R$ is a field using representation-theoretic techniques. In this talk, we will extend the classification to the case of $R$ Noetherian, using results of Gómez and techniques from homotopy theory and both algebraic and tensor-triangular geometry. In particular, over integer coefficients, not every endotrivial arises from a homotopy representation, i.e., an invertible genuine $G$-spectrum. This is joint work with Juan Omar Gómez.