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We discuss finitely graded Iwanaga-Gorenstein (IG) algebras $A$ andrepresentation theory of their (graded) Cohen-Macaulay (CM) modules. Byquasi-Veronese algebra construction, in principle, we may reduce our study tothe case where $A$ is a trivial extension algebra $A = \Lambda \oplus C$ withthe grading $ \text{deg} \Lambda = 0, \ \text{deg} C = 1$. In the previousstudy, we gave a necessary and sufficient condition that $A$ is IG in terms of$\Lambda$ and $C$ by using derived tensor products and derived Homs. Forsimplicity, we assume that $\Lambda$ is of finite global dimension in thesequel. In this paper, we show that the condition that $A$ is IG, has atriangulated categorical interpretation. We prove that if $A$ is IG, then thegraded stable category $\underline{\mathsf{CM}}^{\Bbb{Z}} A$ of CM-modules isrealized as an admissible subcategory of the derived category$\mathsf{D}^{\mathrm{b}}(\text{mod } \Lambda)$. As a corollary, we deduce thatthe Grothendieck group $K_{0}(\underline{\mathsf{CM}}^{\Bbb{Z}} A)$ is free offinite rank.  We give several applications. Among other things, for a path algebra$\Lambda= \Bbb{k} Q$ of an $A_{2}$ or $A_{3}$ quiver Q, we give a complete listof $\Lambda$-$\Lambda$-bimodule $C$ such that $\Lambda \oplus C$ is IG (resp.of finite global dimension) by using the triangulated categoricalinterpretation mentioned above.

On finitely graded Iwanaga-Gorenstein algebras and the stable categories of their (graded) Cohen-Macaulay modules