  Let $\mathcal{G}$ be a split reductive $p$-adic group with connected centre.
We show that each Bernstein block in the principal series of $\mathcal{G}$
admits a definite geometric structure, namely that of an extended quotient. For
the Iwahori-spherical block, this extended quotient has the form $T//W$ where
$T$ is a maximal torus in the Langlands dual group of $\mathcal{G}$ and $W$ is
the Weyl group of $\mathcal{G}$.
