  The group theoretical quantization scheme is reconsidered by means of
elementary systems. Already the quantization of a particle on a circle shows
that the standard procedure has to be supplemented by an additional condition
on the admissibility of group actions. A systematic strategy for finding
admissible group actions for particular subbundles of cotangent spaces is
developed, two-dimensional prototypes of which are T^*R^+ and S^1 x R^+
(interpreted as restrictions of T^*R and T^*S^1 to positive coordinate and
momentum, respectively). In this framework (and under an additional, natural
condition) an SO_+(1,2)-action on S^1 x R^+ results as the unique admissible
group action.
  For symplectic manifolds which are (specific) parts of phase spaces with
known quantum theory a simple projection method of quantization is formulated.
For T^*R^+ and S^1 x R^+ equivalent results to those of more established (but
more involved) quantization schemes are obtained. The approach may be of
interest, e.g., in attempts to quantize gravity theories where demanding
nondegenerate metrics of a fixed signature imposes similar constraints.
