I have a question about fixed points of Galois group actions.
I am hoping that this is easy for the experts.


Let $k$ be a field of characteristic $0$. Let $K$ be a finite 
Galois extension of $k$ with Galois group $G$. 


Supose that $A$ is any finite dimensional $G$-representation over 
$k$. Then $G$ acts diagonally on $A\otimes K$. The question is to 
determine $\dim\_{k}(A\otimes K)^{G}$. I am hoping the answer is 
$\dim\_{k}(A)$. 


Any ideas on how to attack this problem are more than welcomed.



Dimension of fixed points of Galois group actions
This follows from the fact that $K$ is isomorphic as $G$ module to the free module $k[G]$.
(use the existence of a basis of $K$ over $k$ consisting of Galois conjugates.


