Graph product Khintchine inequalities and Hecke C?-algebras: Haagerup inequalities, (non)simplicity, nuclearity and exactness

Graph products of groups were introduced by Green in her thesis [32]. They have an operator algebraic counterpart and explored [14]. In this paper we prove Khintchine type inequalities for general C?-algebraic graph which generalize results Ricard Xu [50] on free C?-algebras. We apply these the context (right-angled) Hecke C?-algebras, are deformations group algebra Coxeter (see [22]). For deduce a Haagerup inequality generalizes from [33]. further use to study simplicity trace uniqueness Lastly characterize exactness nuclearity