  We study functional calculus properties of $C_{0}$-groups on real
interpolation spaces, using transference principles. We obtain interpolation
versions of the classical transference principle for bounded groups and of a
recent transference principle for unbounded groups. Then we show that each
group generator on a Banach space has a bounded $H^{\infty}_{1}$-calculus on
real interpolation spaces. Additional results are derived from this.
