The reaction mechanism for an alpha,beta-unsaturated ketone to react with basic peroxide to form an epoxide is shown below with a general ketone. The basic hydroxide is used to deprotonate the peroxide molecule to create a strong HOO- nucleophile. The peroxide then attacks the beta-carbon of the alkene and this pushes the electrons up to the oxygen of the carbonyl. This is the first intermediate that is formed during this reaction.
After the intermediate is formed, the lone pair from the oxygen pushes back down to form the carbonyl once more and this breaks a carbon-carbon bond which attacks the oxygen of the peroxy group, ultimately substituting an -OH group and forming the final epoxide ketone product.
After the intermediate is formed, the lone pair from the oxygen pushes back down to form the carbonyl once more and this breaks a carbon-carbon bond which attacks the oxygen of the peroxy group, ultimately substituting an -OH group and forming the final epoxide ketone product.