We relate the category of sheaves on alcoves that was constructed in "Sheaves
on the alcoves and modular representations I" to the representation theory of
reductive algebraic groups. In particular, we show that its indecomposable
projective objects encode the simple rational characters of a reductive
algebraic group in all characteristics above the Coxeter number.Comment: 38 pages. Some corrections in version 3. This is the companion
article to "Sheaves on the alcoves and modular representations I". Both
articles replace our earlier submissions arXiv:1508.05579 and
arXiv:1504.0169
