Abstract: Let ? be a finite root system. A ?-graded group is a group G together with a family of subgroups (U?)? ? ? satisfying some purely combinatorial axioms. The main examples of such groups are the Chevalley groups of type ?, which are defined over commutative rings and which satisfy the well-known Chevalley commutator formula. We show that if ? is of rank at least 3, then every ?-graded group is defined over some algebraic structure (e.g. a ring, possibly non-commutative or, in low ranks, even non-associative) such that a generalised version of the Chevalley commutator formula is satisfied. A new computational method called the blueprint technique is crucial in overcoming certain problems in characteristic 2. This method is inspired by a paper of Ronan-Tits.