Subgeometries in the André/Bruck-Bose representation

We consider the André/Bruck-Bose representation of the projective plane PG(2,qn) in PG(2n,q). We investigate the representation of Fqk-sublines and Fqk-subplanes of PG(2,qn), extending the results of [2], [4], [5]. More precisely, we characterise the representation of Fqk-sublines tangent to or contained in the line at infinity, Fq-sublines external to the line at infinity, Fq-subplanes tangent to and Fqk-subplanes secant to the line at infinity.