Dear Gil, we have a nonrational construction with F. Battaglia in the case of simplicial fans here: 	[arXiv:1108.1637][1], where we use foliated compact manifolds instead of toric varieties. In this setting, Stanley's proof of (the necessary part of) the g-conjecture carries over.


  [1]: http://arxiv.org/abs/1108.1637%20%22D.%20Zaffran,%20F.%20Battaglia%3A%20Foliations%20modelling%20nonrational%20simplicial%20toric%20varieties%22