If $G$ is a group scheme of finite type over a field $k$, then one can study it's Hopf Algebra if it is affine. This is clear, but now if $G$ is not affine, one seems to do the following: complete the local ring $\mathcal O_{G,e}$ of the zero point with respect to it's maximal ideal and then one gets a comultiplication on this completion. Furthermore, associate to it the formal group $\hat{G}=Spf(\hat{\mathcal O_{G,e}})$.

As these things (I mean the non-affine case) are not clear to me, I would like to know if there is some more detailed treatment of this anywhere in the literature. I couldn't find anything very satisfying in the standard books.