  The paper studies a higher order unfitted finite element method for the
Stokes system posed on a surface in three-dimensional space. The method employs
generalized Taylor-Hood finite element pairs on tetrahedral bulk mesh to
discretize the Stokes system on embedded surface. Stability and optimal order
convergence results are proved. The proofs include a complete quantification of
geometric errors stemming from approximate parametric representation of the
surface. Numerical experiments include formal convergence studies and an
example of the Kelvin-Helmholtz instability problem on the unit sphere.
