A construction of Gorenstein-projective modules

We determine all the Gorenstein-projective modules over the T2-extension of a Gorenstein algebra, and over , where A and B are self-injective algebras, and M is an A-B bimodule with and MB projective. Using this, we obtain a criterion for the CM-finiteness of the T2-extensions of CM-finite Gorenstein algebras. As an application we get non-trivial examples of CM-finite Gorenstein algebras.