# Is it possible for the Witt group of a scheme to have non-trivial odd torsion?

Let $$F$$ be a field of characteristic not $$2$$. A well-known theorem of Pfister asserts that the torsion of $$W(F)$$, the Witt group of $$F$$, is $$2$$-primary.

Baeza [B, V.6.3] extended this result to Witt groups of semilocal (commutative) rings $$A$$ (assume $$2\in A^\times$$ for simplicity).

Question: Is it known whether the same result holds for arbitrary rings, or more generally, for schemes? Alternatively, are there examples of schemes $$X$$ such that $$W(X)$$ has non-trivial odd torsion?

I am particularly interested in the case where $$X$$ is a real algebraic variety.

The definition of the Witt group of rings and schemes can be found, for instance, in section 1.2 here.

[B] Baeza, Ricardo, Quadratic forms over semilocal rings, Lecture Notes in Mathematics. 655. Berlin-Heidelberg-New York: Springer-Verlag. VI, 199 p. (1978). ZBL0382.10014.