  An l-group G is an abelian group equipped with a translation invariant
lattice order. Baker and Beynon proved that G is finitely generated projective
iff it is finitely presented. A unital l-group is an l-group G with a
distinguished order unit, i.e., an element u in G whose positive integer
multiples eventually dominate every element of G. While every finitely
generated projective unital l-group is finitely presented, the converse does
not hold in general. Classical algebraic topology (a la Whitehead) will be
combined in this paper with the W{\l}odarczyk-Morelli solution of the weak Oda
conjecture for toric varieties, to describe finitely generated projective
unital l-groups.
