  We study orientation data, as introduced by Kontsevich and Soibelman in order
to define well-behaved integration maps from the motivic Hall algebra of
3-dimensional Calabi-Yau categories to rings of motives. We start with an
example that demonstrates the role of orientation data in this story, before
working through the technical details. We give an account of orientation data
in the case of categories of compactly supported sheaves on noncompact
Calabi-Yau three-folds. We finally study how this structure behaves under
pullbacks along quasi-equivalences of categories, prove Kontsevich and
Soibelman's conjecture regarding this behaviour, and also some stronger
theorems regarding flops and more general tilts.
