Abstract: We find counterexamples to a conjecture by Grove, Wilking and Yeager. The conjecture states that if \(M\) is a closed, simply connected \(G\)-manifold, whose quotient \(M/G\) is a hyperbolic polygon, then \(M\) is rationally hyperbolic. The construction of counterexamples consists in performing equivariant connected sums of \(G\)-manifolds, obtaining quotients with an increasing number of sides. By explicit computations in cohomology, we show that the manifolds obtained through this procedure are rationally elliptic, even if their quotients support hyperbolic metrics. This is a joint work with Professor M. Radeschi and A. Minuzzo.