Quadratic representations for groups of Lie type over fields of characteristic two

Suppose K is a field of characteristic two, G is a group of Lie type over K, and V is an irreducible KG-module. By the Steinberg Tensor Product Theorem, V i IVi, where each Vi is an algebraic conjugate of a restricted KG-module. If G contains a quadratically acting fours-group, then I 2. If I=2 or if I=1 and some restrictions are imposed on the fours-group, then a list of the possible restricted modules is able to be determined. In all cases, the restricted modules are fundamental modules and in many cases the majority of these are ruled out.