Homotopy theory of comodules over a Hopf algebroid

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Given a good homology theory E and a topological space X, the E-homology of X is not just an E*-module but also a comodule over the Hopf algebroid (E*, E*E). We establish a framework for studying the homological algebra of comodules over a well-behaved Hopf algebroid (A, Gamma). That is, we construct the derived category Stable(Gamma) of (A, Gamma) as the homotopy category of a Quillen model structure on the category of unbounded chain complexes of Gamma-comodules. This derived category is obtained by inverting the homotopy isomorphisms, NOT the homology isomorphisms. We establish the basic properties of Stable(Gamma), showing that it is a compactly generated tensor triangulated category.