  We discuss finitely graded Iwanaga-Gorenstein (IG) algebras $A$ and
representation theory of their (graded) Cohen-Macaulay (CM) modules. By
quasi-Veronese algebra construction, in principle, we may reduce our study to
the case where $A$ is a trivial extension algebra $A = \Lambda \oplus C$ with
the grading $ \text{deg} \Lambda = 0, \ \text{deg} C = 1$. In the previous
study, 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. For
simplicity, we assume that $\Lambda$ is of finite global dimension in the
sequel. In this paper, we show that the condition that $A$ is IG, has a
triangulated categorical interpretation. We prove that if $A$ is IG, then the
graded stable category $\underline{\mathsf{CM}}^{\Bbb{Z}} A$ of CM-modules is
realized as an admissible subcategory of the derived category
$\mathsf{D}^{\mathrm{b}}(\text{mod } \Lambda)$. As a corollary, we deduce that
the Grothendieck group $K_{0}(\underline{\mathsf{CM}}^{\Bbb{Z}} A)$ is free of
finite 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 list
of $\Lambda$-$\Lambda$-bimodule $C$ such that $\Lambda \oplus C$ is IG (resp.
of finite global dimension) by using the triangulated categorical
interpretation mentioned above.
