Some adjoints in homotopy categories

Let R be a ring. In a previous paper [11] we found a new description for the category K(R-Proj); it is equivalent to the Verdier quotient K(R-Flat)/S, for some suitable S{script} ⊂ K(R-Flat). In this article we show that the quotient map from K(R-Flat) to K(R-Flat)/S{script} always has a right adjoint. This gives a new, fully faithful embedding of K(R-Proj) into K(R-Flat). Its virtue is that it generalizes to nonaffine schemes.