The Grothendieck Group of a Quantum Projective Space Bundle

We compute the Grothendieck group K_0 of non-commutative analogues of quantum projective space bundles. Our results specialize to give the Grothendieck groups of non-commutative analogues of projective spaces, and specialize to recover the Grothendieck group of a usual projective space bundle over a regular noetherian separated scheme. As an application we develop an intersection theory for the quantum ruled surfaces defined by Van den Bergh.