Orbifolds and Orientifolds as O-folds

We consider quotients of string and M-theory by discrete subgroups of the U-duality group. This results in what we call O-folds, which are generalisations of orbifolds and orientifolds, and generically involve non-geometric identifications between physical coordinates and dual winding coordinates. A simple $\mathbb{Z}_2$ quotient encodes the half-maximal duality web, describing on the same footing the Ho\v{r}ava-Witten description of M-theory on an interval, the heterotic theories, and type II in the presence of orientifold planes. This can be analysed using exceptional field theory, including the introduction of extra vector multiplets at the fixed points. This is an overview of the paper [1], based on a talk given at the Corfu Summer Institute 2018.