I'd say an affine algebraic group over $R$ is an $R$-Hopf algebra, that is, a Hopf algebra object in the category of R-R bimodules. Further than that, it's hard for me to say.
I'd say an affine algebraic group over $R$ is an $R$-Hopf algebra, that is, a Hopf algebra object in the category of R-R bimodules. Further than that, it's hard for me to say.