New bases of some Hecke algebras via Soergel bimodules , Advances in Math. 228 (2011) 1043-1067.
This is the first attempt to find explicitly Soergel indecomposable bimodules for extra-large Coxeter systems. This is related to my “Forking Path conjecture” that is false as stated, as proved by Gonzalo Jimenez. Nonetheless, in all generality, there seems to be an extremely strange phenomenon that I would love to understand better.