We study the bundles of generalized theta functions constructed from moduli
spaces of sheaves over abelian surfaces. In degree 0, the splitting type of
these bundles is expressed in terms of indecomposable semihomogeneous factors.
Furthermore, Fourier-Mukai symmetries of the Verlinde bundles are found,
consistently with strange duality. Along the way, a transformation formula for
the theta bundles is derived, extending a theorem of Drezet-Narasimhan from
curves to abelian surfaces