Abstract: Let $k$ be an algebraically closed field of characteristic zero, $B$ the polynomial algebra in $n$ variables over $k$, $D$ a locally nilpotent derivation on $B$ and $A$ the kernel of $D$. A question of Miyanishi asks whether finitely generated projective modules over $A$ are free. It is well known that for $n=2$, i.e., when $B=k[X,Y]$, the kernel $A$ is a polynomial algebra in one variable over $k$. Again, when $n=3$, i.e., when $B= k[X,Y,Z]$, a result of Miyanishi shows that the kernel $A$ is a polynomial algebra in two variables over $k$. Thus, for $n=2$ and $n=3$, Miyanishi's question has an affirmative answer by a theorem of Quillen and Suslin. In my talk I will address Miyanishi's question for $n > 3$. (This is a joint work with S. M. Bhatwadekar and Neena Gupta.)