Stable t-structures and homotopy category of Gorenstein-projective modules

We study the homotopy category of unbounded complexes of Gorenstein-projective modules with bounded relative homologies. We show the existence of a right recollement of the above homotopy category and it has the homotopy category of Gorenstein-acyclic complexes as a triangulated subcategory in some case. We also show that the bounded Gorenstein derived category of a CM-finite Gorenstein artin algebra is triangle equivalent to the bounded derived category of the endomorphism ring of some tilting object.