Gorenstein-projective modules and symmetric recollements

We introduce compatible bimodules. If M is a compatible A–B  -bimodule, then the Gorenstein-projective modules over algebra Λ=(AM0B) are explicitly described; and if Λ is Gorenstein, then this description implies that M is compatible. As an application, if M   is compatible, then there is a left recollement of the stable category GP(Λ)̲; and if Λ   is Gorenstein and MA is projective, then there is a symmetric recollement of the singularity category Dsgb(Λ).