Linearization of group stack actions and the Picard group of the moduli   of $\SL_r/\mu_s$-bundles on a curve
  We first study the descent theory of line bundles under a morphism which is tors or under a group stack and then use this technical result to determine the exact structure of $\Pic(\M_G)$ where $G=\SL_r/\mu_s$ (we include a minor modification to explain the genus 0 case). 
Yves Laszlo