Characteristic classes as obstructions to local homogeneity
  This note is an extended version of my presentation at the "Focused Research Workshop on Exterior Di{\S}erential Systems and Lie Theory" held at the Fields Institute in Toronto, December 9-13, 2013. Some ideas and constructions of this note crystallized during my communication with Anthony D. Blaom. I am deeply grateful to him and also to P.J. Olver for his constant help and encouragement. 
Erc\"ument Orta\c{c}gil
math.AG