For a morphism $f$ of varieties over a field of characteristic $\neq l$ I can consider the functors $Rf_*$, $f^\ast$, $f_!$, and $f^!$ both for the corresponding derived categories of 'all' (constructible?) etale sheaves, or for the categories of $\mathbb{Z}/l\mathbb{Z}$-(constructible?) etale sheaves. There are also the 'forgetful' functors from (the derived categories of) $\mathbb{Z}/l\mathbb{Z}$-sheaves to 'all' (constructible?) sheaves; I guess that these functors possess adjoints.

My question is: do the 'image functors' $Rf_*$, $f^\ast$, $f_!$, and $f^!$ commute with the 'coefficient change' functors mentioned? What are the best references here?