  We consider the tracial crossed product algebra $M=A\rtimes\Lambda$ arising
from a trace preserving action $\sigma:\Lambda \curvearrowright A$ of a
discrete group $\Lambda$ on a tracial von Neumann algebra $A$. For a unitary
subgroup $\mathcal{G}\subset \mathcal{U}(M)$, we study when this $\mathcal{G}$
can be conjugated into $\mathcal{U}(A)\cdot\Lambda$ in $M$. We provide a
general sufficient condition for this to happen. Our result generalizes a
result of Ioana, Popa and Vaes, which treats the case when $M$ is the group von
Neumann algebra $L(\Lambda)$.
