The question is in the title. Maybe I should explain my interest in it though. To every Coxeter group $(W,S)$ (and even more general groups) and a system of parameters $(a_s,b_s)_{s \in S}$ one can attach a Hecke algebra $\mathcal{H}(W,S)$ (this is an exercise in Bourbaki's Groupes et algèbres de Lie IV-VI) with generators $T_w$ ($w \in W$) and relations

$$ \begin{align*} T_w T_{w'} & = T_{ww'} \text{ if } \ell(w)+\ell(w') = \ell(ww') \\ T_s^2 & = a_s + b_s T_s \end{align*} $$

Sometimes, these abstract Hecke algebras turn out to be isomorphic to `convolution type Hecke algebras'

$$ \mathcal{H}(G,B) = \text{End}_G(\text{ind}^G_B \Bbb{1}) $$

for a group $G$ and a subgroup $B$ (I am being deliberately vague here), and one therefore gets a functor $$ \text{Rep}(G) \longrightarrow \text{R-Mod}(\mathcal{H}(W,S)),\quad V \mapsto V^B $$ relating representations of the abstract Hecke algebra and of the group $G$. This is for instance the case if $(W,S)$ comes from a BN-pair (by another Bourbaki exercise).