Compact domination for groups definable in linear o-minimal structures

We prove the Compact Domination Conjecture for groups definable in linear o-minimal structures. Namely, we show that every definably compact group G definable in a saturated linear o-minimal expansion of an ordered group is compactly dominated by (G/G ⁰⁰, m, π), where m is the Haar measure on G/G ⁰⁰ and π : G → G/G ⁰⁰ is the canonical group homomorphism.