It is shown that Suzuki–Ree groups can be easily defined by means of comparing two fundamental representations of the ambient Chevalley group in characteristic 2 or 3. This eliminates the distinction between the Suzuki–Ree groups over perfect and imperfect fields and gives a natural definition for the analogs of such groups over commutative rings. As an application of the same idea, we explicitly construct a pair of polynomial maps between the groups of types (Formula presented.) and (Formula presented.) in characteristic 2 that compose to the Frobenius endomorphism. This, in turn, provides a simple definition for the Tits mixed groups over rings.