How can we view the image of curvature form under invariant polynomial of degree $k$ $f(\Omega)$ as a 2$k$-form?

Question

I'm currently studying from the book of Loring Tu, 'Differential Geometry: Connections, Curvature and Characteristic classes'. chapter 23 sector 2.

what confused me is that I can only view $P(\Omega)$ as a globally defined real-valued function on $M$, how can I view $P(\Omega)$ as a $2k$-form?