  We introduce and investigate the ribbon groupoid associated with a Garside
group. Under a technical hypothesis, we prove that this category is a Garside
groupoid. We decompose this groupoid into a semi-direct product of two of its
parabolic subgroupoids and provide a groupoid presentation. In order to
established the latter result, we describe quasi-centralizers in Garside
groups. All results hold in the particular case of Artin-Tits groups of
spherical type.
