2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68629We develop a general framework to deal with the unitary representations of quantum groups using the language of C*-algebras. Using this framework, we prove that the duality holds in a general context. This extends the framework of the duality theorem using the language of von Neumann algebras previously developed by Masuda and Nakagami.66 pages, no figures LaTeX2e. Accepted to be published by International Journal of MathematicsQuantum Algebra20G42text