Abstract: The affine Weyl group $\widetilde{C}_n$ under a certain
automorphism of $\widetilde{A}_{2n}$ can be seen as a fixed point
set of the affine Weyl group $\widetilde{A}_{2n}$. By giving an
explicit description of the fixed point set of $\widetilde{A}_{2n}$
under this automorphism, we shall give the explicit description of
the cells in weighted Coxeter group $\widetilde{C}_n$ corresponding
to the partition $\bf{2^{n}1}$.

Key words: affine Weyl group, weighted Coxeter group, quasi-split case, partitions of $n$, left cells, two-sided cells