TITLE: Reference for the derived category of $X$, $[X/G]$ and $X/G$
QUESTION [11 upvotes]: I'm trying to learn about derived categories of algebraic stacks. To be honest, as of now, I don't need anything fancy nor deep. In my setup I have a scheme $X$ (well, a smooth and projective variety over $\mathbb{C}$) and a finite group $G$ acting on it. I would like to understand simple things like: what does a coherent sheaf on $[X/G]$ look like? what do the (derived) pushforward functors between the various spaces do? and the pullbacks?
Any pointers would be greatly appreciated!

REPLY [3 votes]: In case anyone is interested, I've been finding this thesis useful
http://tobias-lib.uni-tuebingen.de/volltexte/2007/2941/pdf/diss.pdf