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