According to legend, in the vicinity of Kokshetau were two square related to the name Abylai «Úlken jáne Kishi alany» – large and small square. There is every reason to believe that the main square of Abylay was located in the area «Abylaı hannyń Qyzyl aǵashy». Where about twenty years ago,  at the suggestion of the Kokshetau local historian and founder of the Abylay Khan museum in Burabai , was granite stone was installed with the words of Magzhan Zhumabayev akyn engraved on it:

Ertede jel ótpeıtin Qyzyl Aǵash,

Darıǵa, bul kúnderde jap-jalańash.

Qabirinen áýlıeniń Alashqa artyq,

Ertede Abylaıǵa Orda bolǵan aǵash.

It was on this square surrounded by his like-minded people and comrades-in-arms, the folk batyrs, Kabanbay, Nauryzbay, Bogenbay, Baygazy, Zhanibek, Malaysara, Bayan and many others, Abylay Khan made all important, crucial for the Kazakh steppe decisions. So, according to legend, one of the important decisions that Abylai Khan made at this place is a trip with Khan of the Middle Zhuz Abulmambet and 120 elders in the city of Orenburg to express consent for accepting Russian citizenship.

Here at the «Abylaı hannyń Qyzyl aǵashy» the governor held Kuryltai, military mobilization camps and other large-scale events. The square at the eastern part of the Kokshetau mountain was called «Abylaı han alańy».