Quotienting a curve by finite automorphism subgroup.

Question

Let $Y$ be a smooth projective curve of genus $g$. Let $\Gamma$ be a finite subgroup of the group of automorphisms.

1. What does $Y/{\Gamma}$ mean? I know by GIT we can take good quotients of semistable points under a reduction group action. How can we take quotient of the whole of $Y$?

Let $E$ be a vector bundle on $Y$ and we have $h : Y \to Y/{\Gamma}$.

2. Is $h_{*}E$ a vector bundle on $Y/{\Gamma}$?