  We prove that the operad B of natural operations on the Hochschild cohomology
has the homotopy type of the operad of singular chains on the little disks
operad. To achieve this goal, we introduce crossed interval groups and show
that B is a certain crossed interval extension of an operad T whose homotopy
type is known. This completes the investigation of the algebraic structure on
the Hochschild cochain complex that has lasted for several decades.
