Morally speaking, the Gromov-Witten invariants of a general
symplectic manifold are defined by considering the Euler class of
orbifold vector bundles over orbifolds. Due to the nontriviality of
isotropy groups, these invariants are rational-valued in general.
Following a proposal of Fukaya-Ono back in the 1990s, I will explain
how to construct integral Euler-type cycles for complex vector bundles
over almost complex orbifolds. Combined with a recent result of
Abouzaid-McLean-Smith, this method allows us to define Z-valued
Gromov-Witten invariants in genus 0. This is joint work with Guangbo Xu.