  We study the tensor category $\cQ$ of tilting modules over a quantum group
$U_q$ with divided powers. The set $X_+$ of dominant weights is a union of
closed alcoves $\oC_w$ numbered by the elements $w\in W^f$ of a certain subset
of affine Weyl group $W$. G.Lusztig and N.Xi defined a partition of $W^f$ into
canonical right cells and the right order $\le_R$ on the set of cells. For a
cell $A\subset W^f$ we consider a full subcategory $\cQ_{<A}$ formed by direct
sums of tilting modules $Q(\lambda)$ with highest weights $\lambda \in
\bigcup_{w\in B<_RA} \oC_w$. We prove that $\cQ_{<A}$ is a tensor ideal in
$\cQ$, generalizing H.Andersen's Theorem about the ideal of negligible modules
which in our notations is nothing else then $\cQ_{<\{ e\}}$. The proof is an
application of a recent result by W.Soergel who has computed the characters of
tilting modules.
