"He doffed his Circassian cap"
An Adgyhe man in Constantinople, 1865
Public DomainAn Adgyhe man in Constantinople, 1865

 The Adyghe people, who were called 'Circassians' by Europeans, are an indigenous group from the North Caucasus, on the north-east coast of the Black Sea. In the 1860s, around the time Tolstoy was writing, the Russians were embarking upon a systematic program of ethnic cleansing in this region that saw 90% of the indigenous population deported across the Black Sea to Turkey, where the largest population of Adyghe remains.

Adyghe headgear usually consisted of a tall, conical cap made of Karakul (a type of lamb hide) which was either black or grey in colour. These were called kalpak or papakha.

See here for a wealth of information on Adyghe culture and costume.