A Universal description of global homotopy theory

The passage from the category of spaces to the category of spectra can be desribed by universally `inverting' spheres or equivalently imposing stability. This turns out to be technically very usefuly and philosopically explains why spectra play such an important role. A similar description can be given in equivariant homotopy theory for a fixed Lie group G. We will explain in this talk how such a description can be given for the category of global spectra (which are in some sense equivariant for all Lie groups at the same time) recently studied by Schwede. The description we will give global spectra as cohomology theories on stacks. It also allows us to give methods of constructing such global cohomology theories, for example a global version of TMF (based on a construction of Lurie) or versions of Loop-K-theory.