  We produce full strong exceptional collections consisting of vector bundles
on the geometric invariant theory quotient of certain linear actions of a split
reductive group $G$ of rank two. The vector bundles correspond to irreducible
$G$-representations whose weights lie in an explicit bounded region in the
weight space of $G$. We also describe a method for constructing more examples
of linear GIT quotients with full strong exceptional collections of this kind
as "decorated" quiver varieties.
