  We consider geometrically cellular varieties $X$ over an arbitrary field of
characteristic zero. We study the quotient of the third unramified cohomology
group $H^3_{nr}(X,\mathbb{Q}/\mathbb{Z}(2))$ by its constant part. For $X$ a
smooth compactification of a universal torsor over a geometrically rational
surface, we show that this quotient if finite. For $X$ a del Pezzo surface of
degree $\geq 5$, we show that this quotient is zero, unless $X$ is a del Pezzo
surface of degree 8 of a special type.
