Abstract: The affine Weyl group $(\widetilde{C}_4,\,S)$ can be
considered as the fixed point set of the affine Weyl group
$(\widetilde{A}_7,\,\widetilde{S})$ under a certain group
automorphism $\alpha$. Let
$\widetilde{l}:\widetilde{A}_7\longrightarrow \mathbf{\mathbf{N}}$
be the length function of\,$\widetilde{A}_7$. The restriction of
$\widetilde{l}$ on $\widetilde{C}_4$, denoted by $L$, is a weighted
function on $\widetilde{C}_4$. This paper classified the cells in
weighted Coxteger group\,$(\widetilde{C}_4,\,L)$.

Key words: \!\!affine Weyl group, \!weighted Coxeter group, \!quasi-split case, \!cell, \!\!partition