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Given a group $G$, let $f:A\to B$ be a map between $G$-CW-complexes such that $f^H:A^H\to B^H$ is a homotopy equivalence for every $H\leq G$. Then $f/H:A/H\to B/H$ is also a homotopy equivalence, for any $H \leq G$. The converse, however, is not always true and it is natural to ask when it is true for a given group. In this talk, we give a criterion that guarantees the converse to hold. For this, we construct a model structure on the category of $G$-spaces in which weak equivalences and cofibrations defined on orbits. This is a joint work with Aslı Güçlükan İlhan.