Gorenstein projective objects in comma categories

Let A and B be abelian categories and F : A → B an additive and right exact functor which is perfect, and let ( F , B ) be the left comma category. We give an equivalent characterization of Gorenstein projective objects in ( F , B ) in terms of Gorenstein projective objects in B and A . We prove that there exists a left recollement of the stable category of the subcategory of ( F , B ) consisting of Gorenstein projective objects modulo projectives relative to the same kind of stable categories in B and A . Moreover, this left recollement can be filled into a recollement when B is Gorenstein and F preserves projectives.