  For a formal scheme over a complete discrete valuation ring with a good
action of a finite group, we define equivariant motivic integration, and we
prove a change of variable formula for that.To do so, we construct and examine
an induced group action on the Greenberg scheme of such a formal scheme. Using
this equivariant motivic integration, we define an equivariant volume
Poincar\'e series, from which we deduce Denef and Loeser's motivic zeta
function including the action of the profinite group of roots of unity.
