How to use reduced dimensions (of a PCA) for detection purposes?
Well, mathematically speaking, applying PCA on a bunch of data points usually means (there are some variants) removing the mean and rotate to get uncorrelated features. Then you reduce dimensionality by discarding some of the uncorrelated features.

You may get the corresponding points in the original feature space by doing the inverse rotation and adding the mean back again. Of course, this points now will be contained in a shape of less dimension than before. For example, if you went from 3 original features to 2 uncorrelated features, then perhaps your original data points had some 3D shape, say a football. Then your new points (transformed-inverse transformed) will have the shape of an ellipse.