  We show that near closed points with linearly reductive stabilizer, Artin
stacks are formally locally quotient stacks by the stabilizer. We conjecture
that the statement holds etale locally and we provide some evidence for this
conjecture. In particular, we prove that if the stabilizer of a point is
linearly reductive, the stabilizer acts algebraically on a miniversal
deformation space generalizing results of Pinkham and Rim.
