Let $G$ be an affine algebraic group over $\mathbb{C}$. It is well known that when working with principal $G$ bundles it is too restrictive to require bundles to be locally trivial in the Zariski topology. Instead $G$-bundles are defined to be locally trivial in the etale topology. The finite map $z \to z^n$ from $\mathbb{C}^\times$ to itself is a $\mu_n$ (= $n$th roots of unity) bundle that is not Zariski locally trivial. Also setting $B = Spec \mathbb{C}[s^\pm,t^\pm]$ then $\{x^2 + s y^2 + t z^2 = 0\} \subset \mathbb{P}^2_B$ is a $\mathbb{P}^1$-bundle that gives rise to a $PGL_2$-bundle that is not Zariski locally trivial.

However for some groups (dubbed special groups) being locally trivial in the etale topology implies locally trivial in the Zariski topology. If $G$ is semisimple then Grothendieck proved the only such special $G$ are products of $SL_n$ and $Sp_{2m}$.

**QUESTION**

I would like an example of a non Zariski locally trivial principal $G$-bundle for a simple, simply connected group $G$, e.g. $Spin(n)$ or $G_2$.

My motivation is largely out curiosity. For $G$ as in the question, I study the moduli space of $G$-bundles on a curve (and although for a curve over $\mathbb{C}$ a bundle will be Zariski locally trivial it wont be in families) and I would like to have a non Zariski locally trivial bundle in my back pocket.

A vague idea would be to mimic the $PGL_2$ example above by looking at some varying family of $G/P$. You could try this with $G = E_8$ because it is simply connected and adjoint and if you're lucky you might have $Aut(G/P) = G$. I have no idea if this works but even if it does it would be nice if there was a simpler example.