Geometrical equivalence and action type geometrical equivalence of group representations

In this paper we construct an example of two representations $(V_{1},G_{1})$ and $(V_{2},G_{2})$ which are action type geometrically equivalent and groups $G_{1}$ and $G_{2}$ are geometrically equivalent, but the representations $(V_{1},G_{1})$ and $(V_{2},G_{2})$ are not geometrically equivalent.