Let $R$ be a discrete valuation ring of characteristic $0$ and furthermore let $G$ be a connected, simply connected,split semisimple, affine algebraic group scheme over $R$. Furthermore, let $X$ be a $R$-scheme equipped with a $G$ action $\phi:G \times X \mapsto X$.
What conditions one would like to be imposed on the morphism $\phi$ so that it becomes smooth? I know that in the case of group schemes over a field the condition is that $G$ is smooth. Thank you