Let a finite abelian group G act (linearly) on the space and thus on its complexification . Let W be the real part of the quotient (in general ). We give an algebraic formula for the radial index of a 1‐form on the real quotient W. It is shown that this index is equal to the signature of the restriction of the residue pairing to the G‐invariant part of . For a G‐invariant function f, one has the so‐called quantum cohomology group defined in the quantum singularity theory (FJRW‐theory). We show that, for a real function f, the signature of the residue pairing on the real part of the quantum cohomology group is equal to the orbifold index of the 1‐form on the preimage of W under the natural quotient map.