Orbifold Gromov-Witten theory of weighted blowups

Consider a compact symplectic sub-orbifold groupoid S of a compact symplectic orbifold groupoid (X,omega). Let X(a)be the weight-a blowup of X along S, and D-a= PN(a)be the exceptional divisor, where N is the normal bundle of S in X. In this paper we show that the absolute orbifold Gromov-Witten theory ofX(alpha)can be effectively and uniquely reconstructed from the absolute orbifold Gromov-Witten theories of X, S and D-alpha, the natural restriction homomorphismH*(CR)(X) -> H*(CR)(S) and the first Chern class of the tautological line bundle over D-alpha. To achieve this we first prove similar results for the relative orbifold Gromov-Witten theories of (X-alpha| D-alpha) and (N-alpha| D-alpha). As applications of these results, we prove an orbifold version of a conjecture of Maulik and Pandharipande (Topology, 2006) on the Gromov-Witten theory of blowups along complete intersections, a conjecture on the Gromov-Witten theory of root constructions and a conjecture on the Leray-Hirsch result for the orbifold Gromov-Witten theory of Tseng and You (J Pure Appl Algebra, 2016).