Let X a projective variety over an algebraically closed field on which an abelian variety $A$ acts freely. Then $X/A$ is a projective variety. Let $f:X\rightarrow X/A$

Let $K\in D_{c}^{\leq 0}(X,\bar{\mathbb{Q}}_{l})$ a complex of sheaves not necessarily pure.

We assume that $K$ is equivariant with respect to $A$.

Under which conditions, can we descend $K$ to a complex $K'$ on $X/A$ such that $f^{*}K'=K$.