Quaternionic structures

Any oriented 4-dimensional real vector bundle is naturally a line bundle over a bundle of quaternion algebras. In this paper we give an account of modules over bundles of quaternion algebras, discussing Morita equivalence, characteristic classes and K -theory. The results have been used to describe obstructions for the existence of almost quaternionic structures on 8-dimensional Spin c manifolds in Čadek et al. (2008) [5] and may be of some interest, also, in quaternionic and algebraic geometry.