The unit is named after Adam Kadyrov's call sign, Dustum, which he inherited from his father. Its "Central Base K-13" is located at a facility of the Akhmat special rapid-response unit (SOBR) in Akhmat-Yurt, Ramzan Kadyrov's ancestral village, according to an investigation by Verstka.

The unit is promoted through a dedicated Instagram account. In one video, men in caps bearing the word Dustum practice downing drones and piloting unmanned aerial vehicles; other clips show drill practice, shooting and the evacuation of the wounded. The account's avatar is a neural-network-generated image of Adam shaking hands with the commander of SOBR Akhmat, Timur Edilov.

In 2023, the Chechen state television and radio company reported that Akhmat, Eli and Adam Kadyrov had taken personal control of the reconstruction of a gym and barracks at the facility. A sign reading "Central Base K-13" later appeared on the building. In October 2024, Ramzan Kadyrov published video of Adam conducting a formation of the Akhmat SOBR training center he oversees.

In April, Chechen media began reporting raids on roads by the "city group of the Central Base Dustum K-13." According to Kavkazsky Uzel, the unit's fighters carry them out together with Rosgvardia officers. In one video posted on the base's social media, men in military uniform and Dustum caps demand that drivers remove their window tinting, though they themselves drive tinted SUVs marked "K13."

The unit's combat involvement is not specified.

Other projects are also promoted under Adam Kadyrov's brand. The outlet Komanda K13 advertises the energy drink "K13" and the car-rental service Elite Car 13: its fleet ranges from a G63 Brabus and a Rolls-Royce to a Camry, and payment is accepted only in cash. The rental business is run by the company Elit Kar, whose founder until 2014 was the Kadyrov Foundation. The company is now owned by 23-year-old Minkail Usmanov — a nephew of the wife of Chechnya's head, Medni Kadyrova, and a brother of the republic's deputy prime minister, Anvar Usmanov — and by Adam Seritkhanov, who previously worked in the office of the head and government of Chechnya.

Since 2024, a promotion company, Dustum Boxing, has also operated under Adam's call sign. It is headed by Viktor Khryunov, a relative of the promoter Vladimir Khryunov. According to Verstka's assessment, the company has not had much success — in 2024 a fight for the Russian heavyweight championship fell through because the promoter failed to honor agreements.

Adam Kadyrov became widely known in September 2023, when he beat Nikita Zhuravel, who had been arrested for burning a Quran, in a Grozny pretrial detention center. He subsequently became a Hero of Chechnya twice and received several senior posts in the republic, including secretary of the Security Council and curator of the Interior Ministry. Kadyrov Jr. was also appointed head of his father's security service.

In October 2024, his name was entered in the Russian Book of Records as the youngest head of security service of a regional head — he was 16 at the time. According to a count by Current Time, Kadyrov Jr. has since received more than 20 awards, including the Rosgvardia medal "For Combat Distinction" and the Rosenergoatom gold medal "For Services in Improving the Safety of Nuclear Power Plants." He was also awarded the commemorative medal "90 Years of the Russian Interior Ministry's Traffic Police" — after he caused a fatal road accident in Grozny in January and was himself sent to Moscow for treatment.