  We determine the geometric pro-\'etale cohomology of Drinfeld's upper half
space ${\mathcal X}$ over a p-adic field. The strategy is different from the
one given by Colmez, Dospinescu and Niziol. It uses the approach developed in a
former paper of the author describing global sections of equivariant vector
bundles on ${\mathcal X}$.
