2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/213653A twisted covariant formulation of noncommutative self-dual gravity is presented. The formulation for constructing twisted noncommutative Yang-Mills theories is used. It is shown that the noncommutative torsion is solved at any order of the $θ$-expansion in terms of the tetrad and some extra fields of the theory. In the process the first order expansion in $θ$ for the Plebański action is explicitly obtained.23+1 pages, no figures, corrected typos, references and Appendix B is addedHigh Energy Physics - Theorytext