Cohomology of Burnside Rings

We study the Ext groups groups Ext^l_A(G) (Z_H , Z_J ) where A(G) is the Burnside ring of a finite group G and for a subgroup H ⊂ G, the A(G)-module Z_H is defined by the mark homomorphism corresponding to H. If |G| is square-free we give a complete description of these groups. If |G| is not square-free we show that for certain H, J ⊂ G the groups Ext^l_A(G)(Z_H , Z_J ) have unbounded rank.
We also extend some of these results to the rational and complex rep- resentation rings of a finite group, and describe a new generalisation of the Burnside ring for infinite groups.