Algebraic K-theory of quasi-smooth blow-ups and cdh descent

We construct a semi-orthogonal decomposition on the category of perfect complexes on the blow-up of a derived Artin stack in a quasi-smooth centre. This gives a generalization of Thomasons blow-up formula in algebraic K-theory to derived stacks. We also provide a new criterion for descent in Voevodskys cdh topology, which we use to give a direct proof of Cisinskis theorem that Weibels homotopy invariant K-theory satisfies cdh descent.