  We study the ramification theory for actions involving group schemes,
focusing on the tame ramification. We consider the notion of tame quotient
stack introduced in [AOV] and the one of tame action introduced in [CEPT]. We
establish a local Slice theorem for unramified actions and after proving some
interesting lifting properties for linearly reductive group schemes, we
establish a Slice theorem for actions by commutative group schemes inducing
tame quotient stacks. Roughly speaking, we show that these actions are induced
from an action of an extension of the inertia group on a finitely presented
flat neighborhood. We finally consider the notion of tame action and determine
how this notion is related to the one of tame quotient stack previously
considered.
