Trace minimization with an orthogonality constraint

Question

For positive semi-definite matrices $A,B$, how can I find an $X$ that minimizes $\text{Trace}(AX^TBX$) under the constraint:

that $X$ is orthogonal.

All the matrices have real entries and $A,B$ are square while $X$ is rectangular. Thanks.

This is what I have:

Define $B=F^{T}F$. Define $Y=FX$. You get the above problem as \begin{align} \min_{Y}~ \text{trace}(AY^{T}Y) \end{align}

But now I want $X^*$ that minimizes the original problem. This is what is confusing me!