  The derived category of bounded complexes of coherent sheaves is one of the
most important algebraic invariants of a smooth projective variety. An
important approach to understand derived categories is to construct full
strongly exceptional sequences. The problem of characterizing smooth projective
varieties which have a full strongly exceptional collection and investigate
whether there is one consisting of line bundles is a classical and important
question in Algebraic Geometry. Not all smooth projective varieties have a full
strongly exceptional collection of coherent sheaves. In this paper we give a
structure theorem for the derived category of a toric fiber bundle X over Z
with fiber F provided that F and Z have both a full strongly exceptional
collection of line bundles.
