Cotorsion pairs in C(R-Mod)

In [8] Salce introduced the notion of a cotorsion pair (A, B) in the category of abelian groups. But his definitions and basic results carry over to more general abelian categories and have proved useful in a variety of settings. In this article we will consider complete cotorsion pairs (C,D) in the category C(R-Mod) of complexes of left R-modules over some ring R. If (C ,D) is such a pair, and if C is closed under taking suspensions, we will show when we regard K(C) and K(D) as subcategories of the homotopy category K(RMod), then the embedding functors K(C) → K(R-Mod) and K(D) → K(R-Mod) have left and right adjoints, respectively. In finding examples of such pairs, we will describe a procedure for using Hoveys results in [5] to find a new model structure on C(R-Mod).