(Sorry for my bad English.)
Let $L/K$ be (if necessary finite) Galois extension, and $A$ be $K$-algebra. Then the Galois group $G=\operatorname{Gal}(L/K)$ acts on $K$-algebra $A\otimes_K L$.
So by considering the invariant subring, we get $K$-algebra $(A\otimes_K L)^G\subset A\otimes_K L$.
Now I want if this sub$K$-algebra is isomorphic to $A$?
For example $A=K$ or polynomial ring over $K$ then it's true, but I don't know generally case. Please help me hints, references.