Orbifold Euler characteristics for dual invertible polynomials

To construct mirror symmetric Landau-Ginzburg models, P.Berglund, T.H"ubsch and M.Henningson considered a pair $(f,G)$ consisting of an invertible polynomial $f$ and an abelian group $G$ of its symmetries together with a dual pair $(\tilde{f},\tilde{G})$. Here we study the reduced orbifold Euler characteristics of the Milnor fibres of $f$ and $\tilde{f}$ with the actions of the groups $G$ and $\tilde{G}$ respectively and show that they coincide up to a sign.