2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/164495We construct a compact 6-dimensional solvmanifold endowed with a non-trivial invariant generalized Kähler structure and which does not admit any Kähler metric. This is in contrast with the case of nilmanifolds which cannot admit any invariant generalized Kähler structure unless they are tori.New title. To appear in J. Sympl. GeomDifferential Geometry53C15;22E25;53C56text