Sols Lucía, IgnacioGómez, Tomás L.2023-06-202023-06-2020000373-3505https://hdl.handle.net/20.500.14352/58401Dedicated to Silvio Greco on the occasion of his 60th birthday (Catania, 2001).Let X be a smooth projective complex variety, and let G be an algebraic reductive complex group. We define the notion of principal G-sheaf, that generalises the notion of principal G-bundle. Then we define a notion of semistability, and construct the projective moduli space of semistable principal G-sheaves on X. This is a natural compactification of the moduli space of principal G-bundles. This is the announcement note presented by the second author in the conference held at Catania (11-13 April 2001), dedicated to the 60th birthday of Silvio Greco. Detailed proofs will appear elsewhere.engjournal articlehttp://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/282/259http://www.dmi.unict.it/ojs/index.php/lematematiche/indexopen access512Álgebra1201 Álgebra