  We construct a motivic lift of the action of the Hecke algebra on the
cohomology of PEL Shimura varieties $S_K$. To do so, when $S_K$ is associated
with a reductive algebraic group $G$ and $V$ is a local system on $S_K$ coming
from a $G$-representation, we define a motivic Hecke algebra
$\mathcal{H}^M(G,K)$ as a natural sub-algebra of the endomorphism algebra, in
the triangulated category of motives, of the constructible motive associated
with $S_K$ and $V$. The algebra $\mathcal{H}^M(G,K)$ is such that realizations
induce an epimorphism from it onto the classical Hecke algebra. We then
consider Wildeshaus' theory of interior motives, along with the necessary
hypotheses for it to be employed. Whenever those assumptions hold, one gets a
Chow motive realizing to interior $V$-valued cohomology of $S_K$, equipped with
an action of $\mathcal{H}^M(G,K)$ as an algebra of correspondences modulo
rational equivalence. We give a list of known cases where this applies.
