  From certain triangle functors, called non-negative functors, between the
bounded derived categories of abelian categories with enough projective
objects, we introduce their stable functors which are certain additive functors
between the stable categories of the abelian categories. The construction
generalizes a previous work by Hu and Xi. We show that the stable functors of
non-negative functors have nice exactness property and are compatible with
composition of functors. This allows us to compare conveniently the homological
properties of objects linked by the stable functors. Particularly, we prove
that the stable functor of a derived equivalence between two arbitrary rings
provides an explicit triangle equivalence between the stable categories of
Gorenstein projective modules. This generalizes a result of Y. Kato. Our
results can also be applied to provide shorter proofs of some known results on
homological conjectures.
