Kan. Stat. § 22-4014
If a sentence of execution is suspended by an order of a court, the suspension shall continue until the supreme court orders otherwise. If the sentence is affirmed, the supreme court shall order the execution of the sentence of death and shall designate a week during which the sentence of execution shall be carried out if the week previously designated by the court has passed. Otherwise, the execution shall be carried out during the week previously designated by the court. It shall be the duty of the clerk of the supreme court to issue to the secretary of corrections a warrant under the seal of the court, commanding the secretary or a warden designated pursuant to K.S.A. 22-4001, and amendments thereto, to proceed to carry the sentence into execution during the week designated by the court. The week during which the sentence of execution is to be carried out shall be stated in the warrant. Upon receipt of the warrant it shall be the duty of the secretary of corrections to cause the sentence to be executed as provided by this act during the time designated by the court.
K.S.A. 22-4014