Title: Quaternionic Projective Bundle Theorem and Gysin Triangle in MW-Motivic Cohomology,
Abstract: In this paper, we show that the motive $HP^n$ of the quaternionic
Grassmannian (as defined by I. Panin and C. Walter) splits in the category of
effective MW-motives (as defined by B. Calmès, F. Déglise and J. Fasel).
Moreover, we extend this result to an arbitrary symplectic bundle, obtaining
the so-called quaternionic projective bundle theorem. This enables us to define
Pontryagin classes of symplectic bundles in the Chow-Witt ring.
As an application, we prove that there is a Gysin triangle in MW-motivic
cohomology in case the normal bundle is symplectic.