  We give an equivariant version of the Saito duality which can be regarded as
a Fourier transformation on Burnside rings. We show that (appropriately
defined) reduced equivariant monodromy zeta functions of Berglund-H\"ubsch dual
invertible polynomials are Saito dual to each other with respect to their
groups of diagonal symmetries. Moreover we show that the relation between
"geometric roots" of the monodromy zeta functions for some pairs of
Berglund-H\"ubsch dual invertible polynomials described in a previous paper is
a particular case of this duality.
