Almost $L^{\mathrm{\infty }}$-stability of the Ritz projection for the integral fractional Laplacian with $0<s\le \frac{1}{2}$

For $0<s\le 1\mathrm{/}2$ and $d\ge 1$, the ${\tilde{H}}^s$-projection onto piecewise linear finite element spaces on quasi-uniform meshes of a bounded Lipschitz domain in ${\mathbb{R}}^d$ with a uniform exterior ball condition is almost stable in the maximum norm. The mesh domain need not coincide with the original domain.