  In this paper, a Bondi-Hoyle accretion onto the rotating black hole in
Einstein-Gauss Bonnet gravity is studied. By injecting the gas from the
upstream region of the computational domain, we have found the occurrence of
the stable shock cones in the downstream region. The dynamical structures and
oscillation properties of these shock cones strongly depend on the black hole
spin parameter $a$ and Gauss-Bonnet coupling constant alpha. It is found that
the various values of alpha can lead the different amounts of matter to pile up
close to the black hole horizon, higher alpha causes bigger oscillation
amplitude in the mass accretion rate, and the required time to reach the
steady-state is getting smaller with the increase in alpha. Moreover,
increasing alpha in the negative direction causes a decrease in the shock
opening angle and this angle slightly increases with the increasing $\alpha$ in
the positive direction. We found that the negative values of Gauss-Bonnet
coupling constant are more favored to have interesting physical outcomes such
as accretion rate and oscillation. In addition, the higher the black hole
rotation parameter (a) emerges the higher the accretion rate. It is also
confirmed that, for alpha \rightarrow 0, the black hole solution in EGB gravity
converges to Kerr in general relativity. Furthermore, Gauss-Bonnet coupling
constant could be used to constrain the size of the observed shadow of M87*
radius for various values of the black hole rotation parameter.
