Remarks on a conjecture of Gromov and Lawson
  Gromov and Lawson conjectured that a closed spin manifold M of dimension n with fundamental group pi admits a metric with positive scalar curvature if and only if an associated element in KO_n(B pi) vanishes. In this note we present counter examples to the `if' part of this conjecture for groups pi which are torsion free and whose classifying space is a manifold with negative curvature (in the Alexandrov sense). 
William Dwyer (Notre Dame), Thomas Schick (Uni Goettingen) and Stephan   Stolz (Notre Dame)