Geodesic
Action of groups on real factors of type $\mathrm{III}_\lambda$, $\lambda\ne1$
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 32, Tome 315 (2004), pp. 132-148

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Actions of groups on pure infinite real factors are considered. Actions of discrete amenable group on an injective real factor of type $\mathrm{III}_\lambda$ ($\lambda\ne1$) are classified up to cocycle conjugacy. 
@article{ZNSL_2004_315_a9,
     author = {A. A. Rakhimov},
     title = {Action of groups on real factors of type $\mathrm{III}_\lambda$, $\lambda\ne1$},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {132--148},
     publisher = {mathdoc},
     volume = {315},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2004_315_a9/}
}
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A. A. Rakhimov. Action of groups on real factors of type $\mathrm{III}_\lambda$, $\lambda\ne1$. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 32, Tome 315 (2004), pp. 132-148. http://geodesic.mathdoc.fr/item/ZNSL_2004_315_a9/