Pointwise inner automorphisms of almost periodic factors

We prove that a large class of nonamenable almost periodic type III \(_1\) ${}_1$ factors M, including all McDuff factors that tensorially absorb \(R_\infty \) $R_{\infty }$ and all free Araki–Woods factors, satisfy Haagerup–Størmer’s conjecture (1988): any pointwise inner automorphism of M is the composition of an inner and a modular automorphism.