  Let $L$ be a proper finite extension of the field of $p$-adic numbers and let
$o\subset L$ be its integers, viewed as an abelian locally $L$-analytic group.
Let $\hat{o}$ be the rigid analytic group variety parametrizing the locally
analytic characters of o. We study the Picard group and the Grothendieck group
of this variety. This preprint is in final version, replaces the former
preprint 'Vector bundles over analytic character varieties' and appears in
Manuscripta Mathematica.
