  In the present article we investigate properties of the category of the
integral Grothendieck-Chow motives over a field. We discuss the Krull-Schmidt
principle for integral motives, provide a complete list of the generalized
Severi-Brauer varieties with indecomposable integral motive, and exploit a
relation between the category of motives of twisted flag varieties and integral
$p$-adic representations of finite groups.
