  We study the prime-to-$p$ Hecke action on the projective limit of the sets of
connected components of Shimura varieties with fixed parahoric level at $p$. In
particular, we construct infinitely many Shimura varieties for CM unitary
groups in odd variables for which the considering actions are not transitive.
We prove this result by giving negative examples on the question of
Bruhat--Colliot-Th{\'e}l{\`e}ne--Sansuc--Tits, which is related to the weak
approximation on tori over $\mathbb{Q}$.
