%0 Journal Article %T Cacti and cells %A Ivan Losev %J Mathematics %D 2015 %I arXiv %X The goal of this paper is to construct an action of the cactus group of a Weyl group W on W that is nicely compatible with Kazhdan-Lusztig cells. The action is realized by the wall-crossing bijections that are combinatorial shadows of wall-crossing functors on the category O. %U http://arxiv.org/abs/1506.04400v1