  In this paper we develop the theory of reduction of quantum principal bundles
over projective bases. We show how the sheaf theoretic approach can be
effectively applied to certain relevant examples as the Klein model for the
projective spaces; in particular we study in the algebraic setting the
reduction of the principal bundle $\mathrm{GL}(n) \to \mathrm{GL}(n)/P=
\mathbf{P}^{n-1}(\mathbb{C})$ to the Levi subgroup $G_0$ inside the maximal
parabolic subgroup $P$ of $\mathrm{GL}(n)$. We characterize reductions in the
sheaf theoretic setting.
