Let k be a field. Is there a realization functor
$DM_{gm}(k,\mathbb{Z}/n)^{op} \to D^b_c(k, \mathbb{Z}/n)$
from category of motives to category of complexes of étale sheaves of $\mathbb{Z}/n$ modules with bounded constructible cohomology sheaves?
Let k be a field. Is there a realization functor $DM_{gm}(k,\mathbb{Z}/n)^{op} \to D^b_c(k, \mathbb{Z}/n)$ from category of motives to category of complexes of étale sheaves of $\mathbb{Z}/n$ modules with bounded constructible cohomology sheaves? 


A similar functor, but restricted to the effective part of $DM_{gm}$, is established in Voevodsky's paper on $DM_{gm}$. Actually it is an equivalence (if $n$ is prime to the characteristic of $k$). Also look at Ayoub's paper on etale realization. 

