For finite groups acting on local or global fields, one can describe the structure of tame extensions fairly explicitly. One can extend the notion of ramification for actions of affine group schemes. We will focus on the tame ramification in this context. We will discuss about two definitions of tameness and how they are related. We will see how the fundamental results of ramification theory in algebraic number theory can be translated and when we were able to prove them for action involving group schemes. We get for instance a result describing the inertia group for a tame action. This permits us to induce a tame action by an action of some extension of an inertia group.