By 'work' I would like the correspondence between fiber functors (to finitely generated projective modules) and algebraic groups to be the same as in the field case.

Specifically, if A is an affine ring, and if Proj(A) is the category of finitely generated projective A-modules, when can we say that a fiber functor w:T->Proj(A) corresponds to an algebraic group over A, where T is an A-linear tensor category.