Inductive limits of partial crossed products

Let $((A^{(i)},G,{\alpha }^{(i)}),{\phi }_i{)}_{i\in \mathbb{N}}$ be an inductive sequence of partial dynamical systems. We prove the existence of an induced partial action $\alpha$ of $G$ on the inductive limit $A=\mathrm{}{A}^{(i)}$. We call $\alpha$ the inductive limit partial action. Furthermore, we show the corresponding partial crossed product $A{⋊}_{\alpha }G$ is canonically isomorphic to $\mathrm{}{A}^{(i)}{⋊}_{{\alpha }^{(i)}}G$. We also study the globalization of the inductive limit partial action $\alpha$, its finite Rokhlin dimension and tracial states on $A{⋊}_{\alpha }G$.