Given a smooth projective variety $X$ and a semiample and big $\mathbb{Q}$-divisor $D$. We denote by $R:=\sum_{n\in \mathbb{Z}_{\geq 0}} H^0(X,\mathcal{O}_X(nD))$. Denote by $\tilde R(n)$ the quasi-coherent sheaf on $X$ defined by the $R$-module $R(n)$.
Do in general the isomorphism of sheaves $\tilde R(n) \simeq \mathcal{O}_X(nD)$ holds for each $n\in \mathbb{Z}$?
