  We review the construction (due to Brenner--Schr\"oer) of the Proj scheme
associated with a ring graded by a finitely generated abelian group. This
construction generalizes the well-known Grothendieck Proj construction for
$\mathbb{N}$-graded rings; we extend some classical results (in particular,
regarding quasi-coherent sheaves on such schemes) from the $\mathbb{N}$-graded
setting to this general setting, and prove new results that make sense only in
the general setting of Brenner--Schr\"oer. Finally, we show that flag varieties
of reductive groups, as well as some vector bundles over such varieties
attached to representations of a Borel subgroup, can be naturally interpreted
in this formalism.
