  It is shown that the values of Harish-Chandra distribution characters on
definable compact subsets of the set of topologically unipotent elements of
symplectic or special orthogonal p-adic groups can be expressed as the trace of
Frobenius action on virtual Chow motives. The result is restricted to a class
of depth-zero representations that can be obtained by inflation from
Deligne-Lusztig representations. The proof relies on arithmetic motivic
integration.
