  In his theory of unipotent characters of finite groups of Lie type, Lusztig
constructed modular categories from two-sided cells in Weyl groups.
Brou\'e,Malle and Michel have extended parts of Lusztig's theory to complex
reflection groups. This includes generalizations of the corresponding fusion
algebras, although the presence of negative structure constants prevents them
from arising from modular categories. We give here the first construction of
braided pivotal monoidal categories associated with non-real reflection groups
(later reinterpreted by Lacabanne as super modular categories). They are
associated with cyclic groups, and their fusion algebras are those constructed
by Malle.
