Let $X$ be a scheme define over $\mathbb{C}$ with an involution $\sigma$. Then how to get a $X_{\mathbb{R}}$ scheme define over $\mathbb{R}$ such that $X_{\mathbb{R}}\times_\mathbb{R} \mathbb{C} = X$ ? How the real algebraic bundle on $X_{\mathbb{R}}$ and complex bundle on $X$ are related?