Witt invariants of quaternionic forms

We describe all Witt invariants of anti-hermitian forms over a quaternion algebra with its canonical involution, and in particular all Witt invariants of orthogonal groups O(A,σ) where (A,σ) is an central simple algebra with orthogonal involution and A has index $2$. They are combinations of appropriately defined λ-powers, similarly to the case of quadratic forms, but the module of invariants is no longer free over those operations. The method involves extending the scalars to a generic splitting field of A, and controlling the residues of the invariants with respect to valuations coming from closed points in the Severi-Brauer variety.