On the derived category of quasi-coherent sheaves on an Adams geometric stack

Let X be an Adams geometric stack. We show that D(Aqc(X)), its derived category of quasi-coherent sheaves, satisfies the axioms of a stable homotopy category defined by Hovey, Palmieri and Strickland in [13]. Moreover we show how this structure relates to the derived category of comodules over a Hopf algebroid that determines X.