Semi-continuit\'e des cellules de Kazhdan-Lusztig
  Computations in small Coxeter groups and infinite dihedral groups suggest that Kazhdan-Lusztig cells for unequal parameters obey to some "semicontinuity" phenomenon (as the parameter vary). The aim of this paper is to provide a rigorous theoretical background that allows to state some precise conjectures. 
C\'edric Bonnaf\'e (LM-Besan\c{c}on)