We establish curious Lefschetz property for generic character varieties of Riemann surfaces conjectured by Hausel, Letellier and Rodriguez-Villegas. Our main tool applies directly in the case when there is at least one puncture where the local monodromy has distinct eigenvalues. We pass to a vector bundle over the character variety, which is then decomposed into cells, which look like vector bundles over varieties associated to braids by Shende-Treumann-Zaslow. These varieties are in turn decomposed into cells that look like (C∗)d−2k×Ck. The curious Lefschetz property is shown to hold on each cell, and therefore holds for the character variety. To deduce the general case, we introduce a fictitious puncture with trivial monodromy, and show that the cohomology of the character variety where one puncture has trivial monodromy is isomorphic to the sign component of the Sn action on the cohomology for the character variety where trivial monodromy is replaced by regular semisimple monodromy. This involves an argument with the Grothendieck-Springer sheaf, and analysis of how the cohomology of the character variety varies when the eigenvalues are moved around.