Involutions of Exceptional Geometries of Type E7

An involution of an exceptional geometry of type E7 is called regular if its fix structure, viewed as simplicial complex, is a building. Involutions which do not act trivially on the underlying field correspond to Galois descent and were treated a long time ago by Jacques Tits. In the present paper, we classify the regular involutions of geometries of type E7 that act trivially on the underlying (arbitrary) field, which we assume not to have characteristic 2. As a result, we discover new subgeometries of the exceptional geometry of type E7.