0P23 Corollary 4.8. Given (W,S)(W,S) a finite Coxeter group and b∈BSb\in B_{S}, let NS(Fb)=HH∗−|S|+l(b)2S(Fb)[|S|+l(b)2]∈D12b(PS−modgr)12𝐙.N_{S}(F_{b})=\operatorname{HH}\nolimits_{*-\frac{|S|+l(b)}{2}}^{S}(F_{b})\left[\frac{|S|+l(b)}{2}\right]\in D^{b}_{\frac{1}{2}}(P_{S}\operatorname{\!-modgr}\nolimits)^{\frac{1}{2}{\mathbf{Z}}}. • We have NS(FbFb′)≃NS(Fb′Fb)N_{S}(F_{b}F_{b^{\prime}})\simeq N_{S}(F_{b^{\prime}}F_{b}) for all b,b′∈BSb,b^{\prime}\in B_{S}. • Given s∈Ss\in S and b∈BS∖sb\in B_{S\setminus s}, we have NS(γS∖s(Fb)Fs±1)≃ρS∖s∗NS∖s(Fb)N_{S}(\gamma_{S\setminus s}(F_{b})F_{s}^{\pm 1})\simeq\rho_{S\setminus s}^{*}N_{S\setminus s}(F_{b}).