  We describe the singular cohomology ring, the K-ring of complex vector
bundles, the Chow ring, and the Grothendieck ring of coherent sheaves of the
total space of the fibre bundle with base space an irreducible nonsingular
complete Noetherian scheme and fibre a nonsingular projective T-toric variety
associated to a prinicipal T-bundle over the field of complex numbers.
