  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.
