  Let $G$ denote a countable inverse semigroup. We construct a kind of a
Baum--Connes map $K(\tilde A \rtimes G) \rightarrow K(A \rtimes G)$ by a
categorial approach via localization of triangulated categories, developed by
R. Meyer and R. Nest for groups $G$. We allow the coefficient algebras $A$ to
be in a special class of algebras called fibered $G$-algebras. This note
continues and fixes our preprint "Attempts to define a Baum--Connes map via
localization of categories for inverse semigroups".
