  Let $\mathbb{k}$ be an algebraically closed field. Connections between
representations of the generalized Kronecker quivers $K_r$ and vector bundles
on $\mathbb{P}^{r-1}$ have been known for quite some time. This article is
concerned with a particular aspect of this correspondence, involving more
generally Steiner bundles on Grassmannians $\mathrm{Gr}_d(\mathbb{k}^r)$ and
certain full subcategories $\mathrm{rep}_{\mathrm{proj}}(K_r,d)$ of relative
projective $K_r$-representations. Building on a categorical equivalence first
explicitly established by Jardim and Prata, we employ representation-theoretic
techniques provided by Auslander-Reiten theory and reflection functors to
organize indecomposable Steiner bundles in a manner that facilitates the study
of bundles enjoying certain properties such as uniformity and homogeneity.
Conversely, computational results on Steiner bundles motivate investigations in
$\mathrm{rep}_{\mathrm{proj}}(K_r,d)$, which elicit the conceptual sources of
some recent work on the subject.
  From a purely representation-theoretic vantage point, our paper initiates the
investigation of certain full subcategories of the, for $r\!\ge\!3$, wild
category of $K_r$-representations. These may be characterized as being right
Hom-orthogonal to certain algebraic families of elementary test modules.
