Let's denote $G$-$Gpd$ the presheaf category $[BG, Gpd]$. Now assume that $Gpd$ is endowed with its natural model structure where weak equivalences are equivalences of groupoids. There is a natural candidate for a model structure on $G$-$Gpd$ where a map in $G$-$Gpd$ is a weak equivalence (resp. a fibration) iff for every subgroup $H$ of $G$ its restriction to $H$-invariants is a weak equivalence of groupoids (resp. a fibration of groupoids). A sufficient condition for the existence of this model structure is: the $H$-fixed points functors have to be cellular for every subgroup $H$ of $G$. This condition means that these functors have to preserve some pushouts and some directed colimits. The details on the cellularity condition are available here Def 3.7 http://www.math.uiuc.edu/~bertg/EquivModels.pdf . It is well-known that this condtion is satisfied if one starts with the Quillen model structure on simplicial sets. I have also read that it is true for Thomason model structure on $Cat$. Is the cellularity condition satisfied if one starts with the natural model structure on $Gpd$ ? If yes, where I can find a reference ? Thanks