  Grothendieck-Birkhoff Theorem states that every finite dimensional vector
bundle over the projective line P1 splits as the sum of one dimensional vector
bundles. This can be rephrased, in terms of orders, as stating that all maximal
orders over the projective line in a matrix algebra split. In this work we
study the extent to which this result can be generalized to Eichler orders when
the base field F is finite. To be precise, we characterize both the genera of
Eichler orders containing only split orders and the genera containing only a
finite number of non-split conjugacy classes. The latter characterization is
given for arbitrary projective curves over F. The method developed here also
allows us to compute quotient graphs for some subgroups of $PGL_2(F[t])$ of
arithmetical interest.
  This paper includes material from the unpublished work "Simultaneous
diagonalization of vector bundles".
