Quivers, vector bundles and coverings of smooth curves

Fix a finite quiver $Q$ and consider quiver-bundles on smooth and connected projective curves. Let $f\colon X\to Y$ be a degree $m$ morphism between such curves and $\tilde E$ a quiver bundle on $Y$. We prove that $\tilde E$ is semistable (resp. polystable) if and only if $f^\ast (\tilde E)$ is semistable. Then we construct many stable quiver-bundles on bielliptic curves.