Which of the algae groups contain the same photosynthetic pigments as green plants, have lots of cellulose in their cell walls, and polymerize sugar to make starch, just like modern plants?

Green Algae

Explanation:

Green algae (sing. alga) come in a heteromorph group of species and this is only a conventional name rather than biological classification. The group unites some predominant divisions like Chlorophyta and Charophyta. Some species of Chlorophyta are considered to be the first ‘true’ plants by bridging between Protozoa and Plantae. Most of this division’s representatives are aquatic, they have chloroplasts and chlorophyll a and b, which are typical for plants. They could be unicellular, often colonial and even multicellular. The variety of the group is great in terms of their habitat, morpho-structure, reproductive system, etc. Some even live in symbiosis with fungi, but they are usually classified in a different division called Lichenophyta. Hence, the answer is "green algae"

Genetic engineering is the answer.