We prove the existence of torus invariant almost complex structure on any positively omnioriented four dimensional primitive quasitoric orbifold. We construct pseudo-holomorphic blowdown maps for such orbifolds. We prove a version of McKay correspondence when the blowdowns are crepant.
"Blowdowns and McKay correspondence on four dimensional quasitoric orbifolds." Osaka J. Math. 50 (2) 397 - 415, June 2013.