We describe all Witt invariants and mod 2 cohomological invariants of the functor as combinations of fundamental invariants; this is related to the study of operations on mod 2 Milnor K-theory. We also study behaviour of these invariants with respect to products, restrictions, similitudes and ramification.
"Witt and cohomological invariants of Witt classes." Ann. K-Theory 5 (2) 213 - 248, 2020. https://doi.org/10.2140/akt.2020.5.213