In this work we describe the Chen-Ruan cohomology of the moduli stack of smooth and stable genus 2 curves with marked points. In the first half of the paper we compute the additive structure of the Chen-Ruan cohomology ring for the moduli stack of stable n-pointed genus 2 curves, describing it as a rationally graded vector space. In the second part we give generators for the even Chen-Ruan cohomology ring as an algebra on the ordinary cohomology.
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