Center of ${\mathcal{H}}_R(0,c_{\tilde{s}})$ associated to a pro-$p$-Iwahori Weyl group

Let $W$ be an Iwahori Weyl group and $W(1)$ be an extension of $W$ by an abelian group. Vigneras gave a description of the $R$-algebra ${\mathcal{H}}_R(q_{\tilde{s}},c_{\tilde{s}})$ associated to $W(1)$, and also gave a basis of the center of ${\mathcal{H}}_R(q_{\tilde{s}},c_{\tilde{s}})$ using the Bernstein presentation of $$\mathcal{H}$R(q{\tilde{s}}, c_{\tilde{s}})$\mathrm{.}Inthispaper,werestricttothecasewhere$q_{\tilde{s}}=0$andusetheIwahori-Matsumotopresentationtogiveabasisofthecenterof$$\mathcal{H}$R(0, c{\tilde{s}})$.