2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/33423The notions of Busby-Smith and Green type twisted actions are extended to discrete unital inverse semigroups. The connection between the two types, and the connection with twisted partial actions, are investigated. Decomposition theorems for the twisted crossed products are given.31 pages, Plain TeX. J. Operator Theory (to appear)Functional AnalysisOperator Algebras46L55text