We construct manifolds and orbifolds with quasitoric boundary. We show that these manifolds and orbifolds with boundary has a stable complex structure. These induce explicit (orbifold) complex cobordism relations among quasitoric manifolds and orbifolds. In particular, we show that a quasitoric orbifold is complex cobordant to some copies of fake weighted projective spaces. The famous problem of Hirzebruch is that which complex cobordism classes in $\Omega^U$ contain connected nonsingular algebraic varieties? We give some sufficient conditions to show when a complex cobordism class may contains an almost complex quasitoric manifold. Andrew Wilfong give some necessary condition of this problem up to dimension 8.