We known that there exists smooth integer homology n-sphere (n>4) with some non-trivial fundamental group by the Kervaire theorem [Michel A. Kervaire, MR 253347 Smooth homology spheres and their fundamental groups, Trans. Amer. Math. Soc. 144 (1969), 67--72.]
(1) Have another examples about that?
(2) Is it possible that some aspherical manifolds are higher-dimensions integer homology spheres?---Asked by Thurston and Kan.
Remark: As far as I know, Andrejz Szczepanski [Aspherical manifolds with the Q-homology of a sphere] proved (2) in the odd dimensions, but it is the rationnal homology sphere. And it is also true in the 3-dimension and 4-dimension, see [John G. Ratcliffe and Steven T. Tschantz, MR 2114711 Some examples of aspherical 4-manifolds that are homology 4-spheres, Topology 44 (2005), no. 2, 341--350.]