  We show the $\TT^2$-cobordism group of the category of 4-dimensional
quasitoric manifolds is generated by the $\TT^2$-cobordism classes of $\CP^2$.
We construct nice oriented $\TT^2$ manifolds with boundary where the boundary
is the Hirzebruch surfaces. The main tool is the theory of quasitoric
manifolds.
