Geodesic
Smooth and piecewise-linear structures on products of projective spaces
Izvestiya. Mathematics , Tome 22 (1984) no. 2, pp. 339-355.

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Several theorems are proved, showing the nonrealizability of certain elements of Wall groups of elementary $2$-groups by normal maps of closed manifolds. Using these results, the classification of homotopy triangulations of products of projective spaces is obtained. Bibliography: 13 titles. 
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A. F. Kharshiladze. Smooth and piecewise-linear structures on products of projective spaces. Izvestiya. Mathematics , Tome 22 (1984) no. 2, pp. 339-355. http://geodesic.mathdoc.fr/item/IM2_1984_22_2_a8/

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[2] Wall C. T. C., “Some $L$-groups of finite groups”, Bull. Amer. Math. Soc., 79:3 (1973), 526–529 | DOI | MR | Zbl

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[4] Sullivan D., Geometric Topology Notes, Princeton, 1967

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[10] Kharshiladze A. F., “Prepyatstviya k perestroikam dlya gruppy $(\pi\times Z_2)$”, Matem. zametki, 16:5 (1974), 823–832 | Zbl

[11] Kharshiladze A. F., “Mnogoobraziya gomotopicheskogo tipa proizvedeniya dvukh proektivnykh prostranstv”, Matem. sbornik, 96(138):4 (1975), 507–522 | MR | Zbl

[12] Kharshiladze A. F., “Ermitova $K$-teoriya i kvadratichnye rasshireniya kolets”, Tr. MMO, 41, 1980, 5–36 | MR

[13] Kharshiladze A. F., “Konstruktsiya razlichayuschei v ermitovoi $K$-teorii”, UMN, 34:6(210) (1979), 204–207 | MR | Zbl