Regular bi-interpretability of Chevalley groups over local rings

We prove that if G(R) = G_π(Φ , R) (E(R) = E_π(Φ , R)) is an (elementary) Chevalley group of rank > 1 , R is a local ring (with 12 for the root systems A₂, B_l, C_l, F₄, G₂ and with 13 for G₂) , then the group G(R) (or (E(R)) is regularly bi-interpretable with the ring R. As a consequence of this theorem, we show that the class of all Chevalley groups over local rings (with the listed restrictions) is elementarily definable, i.e., if for an arbitrary group H we have H≡ G_π(Φ , R) , then there exists a ring R^′≡ R such that H≅ G_π(Φ , R^′) .