  We prove that under some assumptions on an algebraic group $G$,
indecomposable direct summands of the motive of a projective $G$-homogeneous
variety with coefficients in $\mathbb{F}_p$ remain indecomposable if the ring
of coefficients is any field of characteristic $p$. In particular for any
projective $G$-homogeneous variety $X$, the decomposition of the motive of $X$
in a direct sum of indecomposable motives with coefficients in any finite field
of characteristic $p$ corresponds to the decomposition of the motive of $X$
with coefficients in $\mathbb{F}_p$. We also construct a counterexample to this
result in the case where $G$ is arbitrary.
