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

An asymptotic cell category for cyclic groups