The motivic Steenrod algebra in positive characteristic

Let S be an essentially smooth scheme over a field and ℓ ≠D char S a prime number. We show that the algebra of bistable operations in the mod ℓ motivic cohomology of smooth S-schemes is generated by the motivic Steenrod operations. This was previously proved by Voevodsky for S a field of characteristic zero. We follow Voevodsky's proof but remove its dependence on characteristic zero by using életale cohomology instead of topological realization and by replacing resolution of singularities with a theorem of Gabber on alterations.