  Let D be a central division algebra over a field F. We study in this note the
rigidity of the motivic decompositions of the Severi-Brauer varieties of D,
with respect to the ring of coefficients and to the base field. We first show
that if the ring of coefficient is a field, these decompositions only depend on
its characteristic. In a second part we show that if D remains division over a
field extension E/F, the motivic decompositions of several Severi-Brauer
varieties of D remain the same when extending the scalars to E.
