  The paper studies a geometrically unfitted finite element method (FEM), known
as trace FEM or cut FEM, for the numerical solution of the Stokes system posed
on a closed smooth surface. A trace FEM based on standard Taylor-Hood
(continuous P2-P1) bulk elements is proposed. A so-called volume normal
derivative stabilization, known from the literature on trace FEM, is an
essential ingredient of this method. The key result proved in the paper is an
inf-sup stability of the trace P2-P1 finite element pair, with the stability
constant uniformly bounded with respect to the discretization parameter and the
position of the surface in the bulk mesh. Optimal order convergence of a
consistent variant of the finite element method follows from this new stability
result and interpolation properties of the trace FEM. Properties of the method
are illustrated with numerical examples.
