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The compact simply connected Riemannian 4-symmetric spaces were classified byJ.A. Jim{\'{e}}nez. As homogeneous manifolds, these spaces are of the $G/H$,where $G$ is a connected compact simple Lie group with an automorphism$\tilde{\gamma}$ of oder 4 and $H$ is a fixed points subgroup $G^\gamma$ of$G$. In the present article, for the exceptional compact Lie group $G=E_8$, wegive the explicit form of automorphism of order 4 induced by the$\boldsymbol{R}$-linear transformation $\sigma'_{4}$ and determine thestructure of the group $(E_8)^{\sigma'_{4}}$. Thereby, we realize the globallyexceptional Riemannian $4$-symmetric space $E_8/(E_8)^{\sigma'_{4}}$.

Realization of globally exceptional Riemannian $4$-symmetric space $E_8/(E_8)^{\sigma'_{4}}$