  We show that K3 surfaces with non-symplectic automorphisms of prime order can
be used to construct new compact irreducible G2-manifolds. This technique was
carried out in detail by Kovalev and Lee for non-symplectic involutions. We use
Chen-Ruan orbifold cohomology to determine the Hodge diamonds of certain
complex threefolds, which are the building blocks for this approach.
