2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/164224We compute two-sided cells of Weyl groups of type $B$ for the "asymptotic" choice of parameters. We also obtain some partial results concerning Kazhdan-Lusztig conjectures in this particular case.20 pages, some misprints have been cleaned up in this second versionRepresentation Theory20C08 (Primary) 20C15 (Secondary)Two-sided cells in type $B$ (asymptotic case)text