  Mimetic gravity is analysed in the framework of some extensions of General
Relativity, where a function of the Gauss-Bonnet invariant in four dimensions
is considered. By assuming the so-called mimetic condition, the conformal
degree of freedom is isolated and a pressureless fluid naturally arises. Then,
the complete set of field equations for mimetic Gauss-Bonnet gravity is
established and some inflationary models are analysed, for which the
corresponding gravitational action is reconstructed. The spectral index and
tensor-to-scalar ratio are obtained and compared with observational bounds from
Planck and BICEP2/Keck array data. The full agreement with above data is
achieved for several versions of the mimetic Gauss-Bonnet gravity. Finally,
some extensions of Gauss-Bonnet mimetic gravity are considered and the
possibility of reproducing inflation is also explored.
