Automorphisms of a Chevalley group of type $\mathbf G_2$ over a commutative ring $R$ with $1/3$ generated by the invertible elements and $2R$

In this paper, we prove that every automorphism of a Chevalley group with the root system $\mathbf G_2$ over a commutative ring $R$ with $1/3$ generated by the invertible elements and the ideal $2R$ is a composition of ring and inner automorphisms.