In this note, for a compact subgroup H of locally compact topological group G, we consider the homogeneous space G/H equipped with strongly quasi-invariant Radon measure µ which arises from a rho-function. We show that for each φ in the spectrum of L1(G/H), the Banach algebra L1(G/H) is right φ-contractible if and only if G/H is compact. When H is normal in G, this implies that L1(G) is character contractible if and only if G is finite.
