Quasi-isometric free group representations into <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mo form="prefix">SL</mml:mo> <mml:mn>3</mml:mn> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>ℝ</mml:mi> <mml:mo>

We study quasi-isometric representations of finitely generated non-abelian free groups into some higher rank semi-simple Lie groups which are not Anosov, nor approximated by Anosov. We show in some cases that these can be perturbed to be non-quasi-isometric, or to have some instability properties with respect to their action on the flag space.