  We construct, based on Nicaise's article in Math. Ann. in 2009, an
equivariant geometric motivic integration for special formal schemes, such that
when applying to algebraizable formal schemes, we can revisit our previous work
in 2020 on equivariant motivic integration for algebraic varieties. We prove
the change of variable formula for the integral by pointing out the existence
of an equivariant N\'eron smoothening for a flat generically smooth special
formal scheme. We also define the motivic Milnor fiber of a formal power series
and predict that it is the right quantity to define the motivic Milnor fiber of
a germ of complex analytic functions.
