The L-group of a covering group

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We incorporate nonlinear covers of quasisplit reductive groups into the Langlands program, defining an L-group associated to such a cover. This L-group is an extension of the absolute Galois group of a local or global field F by a complex reductive group. The L-group depends on an extension of a quasisplit reductive F-group by K₂, a positive integer n (the degree of the cover), an injective character ε μₙ → C×, and a separable closure of F. Our L-group is consistent with previous work on covering groups, and its construction is contravariantly functorial for certain well-aligned homomorphisms. An appendix surveys torsors and gerbes on the étale site, as they are used in a crucial step in the construction.