Star of Kobol
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The Star of Kobol is an award bestowed at the Quorum of Twelve's discretion. According to Sire Domra in his speech to Commander Adama, such an award was an honor that no "living Colonist had been given in over a millennium".
The Quroum gave this award to Adama in order to sugarcoat the fact that they were relieving Adama over unilaterial control of the Fleet (Baltar's Escape).