  In this paper, we first remind how we can see the "hull" of the pinwheel
tiling as an inverse limit of simplicial complexes (Anderson and Putnam) and we
then adapt the PV cohomology introduced in a paper of Bellissard and Savinien
to define it for pinwheel tilings. We then prove that this cohomology is
isomorphic to the integer \v{C}ech cohomology of the quotient of the hull by
$S^1$ which let us prove that the top integer \v{C}ech cohomology of the hull
is in fact the integer group of coinvariants on some transversal of the hull.
The gap-labelling for pinwheel tilings is then proved and we end this article
by an explicit computation of this gap-labelling, showing that $\mu^t
\big(C(\Xi,\ZZ) \big) = \dfrac{1}{264} \ZZ [\dfrac{1}{5}]$.
