Abstract: Classically, the Bass?Heller?Swan decomposition relates algebraic K-theory of a Laurent polynomial ring to algebraic K-theory of its coefficient ring. In this talk, I will explain how to obtain a generalisation of this result in the setting of localising invariants of stable infinity-categories that come with an automorphism. Furthermore, I?ll explain regularity conditions under which the relevant assembly map is an equivalence. As an application one gets a splitting result for Waldhausen?s A-theory of mapping tori. Based on joint work with Christian Kremer.