Etale devissage, descent and pushouts of stacks

We show that the pushout of an kale morphism and an open immersion exists in the category of algebraic stacks and show that such pushouts behave similarly to the gluing of two open substacks. For example, quasi-coherent sheaves on the pushout can be described by a simple gluing procedure. We then outline a powerful devissage method for representable kale morphisms using such pushouts. We also give a variant of the devissage method for representable quasi-finite flat morphisms.