In this paper, starting from a \(C^{*}\)-probability space \(\mathfrak {X}_{\varphi } \) generated by mutually free, countable-infinitely many semicircular elements \(\{s_{n}\}_{n=1}^{\infty }\), the free distributional data on \(\mathfrak { X}_{\varphi }\) are characterized by joint free moments of \(\{s_{n}\}_{n=1}^{\infty }\); and then, a certain group \(\lambda \) acting on \( \mathfrak {X}_{\varphi }\) is constructed-and-studied under a group dynamical system \(\Gamma \) of \(\lambda \). From the dynamics, the crossed product \( C^{*}\)-algebra \(\mathbb {X}\Gamma \) is constructed, and the free probability on \(\mathbb {X}\Gamma \) is considered in terms of that on \(\mathfrak {X}_{\varphi }\). In particular, the free-distributional data of generating operators of \(\mathbb {X} \Gamma \) are studied, and they illustrate how semicircularity works under our group-action.