KMS states on the C*-algebras of Fell bundles over étale groupoids

Let p: A -> G be a saturated Fell bundle over a locally compact, Hausdorff, second countable, &tale groupoid G, and let C*(G;A) denote its full C*-algebra. We prove an integration-disintegration theorem for KMS states on C*(G; A) by establishing a one-to-one correspondence between such states and fields of measurable states on the C*-algebras of the Fell bundles over the isotropy groups. This correspondence is established for certain states on C*(G; A) also. While proving this main result, we construct an induction C*-correspondence between C*(G; A) and the C*-algebra of an isotropy Fell bundle. We illustrate our results through many examples, such as groupoid crossed products, twisted groupoid crossed products and matrix algebras M-n(C(X)) circle times A.